L& H23I 



A STUDY OF THE RELATION OF SOME 
PHYSIGAL DEFEGTS TO ACHIEVE- 
MENT IN THE ELEMENTARY 
SGHOOL 



BY 

JASPER N. MALLORY, PH. D. 



GEORGE PEABODY GOLLEGE FOR TEACHERS 

CONTRIBUTION TO EDUCATION 

NUMBER NINE 




PUBLISHED UNDER THE DIRECTION OF 

GEORGE PEABODY COLLEGE FOR TEACHERS 

NASHVILLE, TENN. 
1922 

MOTlOTT&Pb 



A STUDY OF THE RELATION OF SOME 
PHYSICAL DEFECTS TO ACHIEVE- 
MENT IN THE ELEMENTARY 
SCHOOL 



BY 

JASPER NiMALLORY, PH. D. 



GEORGE PEABODY GOLLEGE FOR TEACHERS 

CONTRIBUTION TO EDUCATION 

NUMBER NINE 




PUBLISHED UNDER THE DIRECTION OF 

GEORGE PEABODY COLLEGE FOR TEACHERS 

NASHVILLE, TENN. 

1922 






*w 




ACKNOWLEDGMENTS 

Grateful acknowledgment is here made to Dr. Shelton 
Phelps, under whose direction this study has been made ; to 
Dr. W. P. Ott, Professor of Mathematics, Vanderbilt Uni- 
versity, for instruction in the Theory of Probabilities ; and 
to Dr. Norman Frost, Dr. Joseph Peterson, and other pro- 
fessors of George Peabody College, from whom many val- 
uable suggestions were received. Thanks are. also extended 
to Superintendent H. H. Ellis, of Humboldt, for permitting 
the data to be collected in his school. Acknowledgment is 
also made to Prof. L. D. Rutledge, of Union University, who 
collaborated with the writer in the collection of the data, 
and to Miss E. N. Sanborn, R. P. H. N., who administered 
the physical examinations. J. N. M. 



CONTENTS 



Introduction 

Historical Background for Present Movements in Health Super- 
vision 



7 



Chapter I 
Previous Objective Studies of Related Subjects 11 

Chapter II 
The Purpose and Scope of the Present Study 19 

Chapter III 
Material and Methods Used in This Study 22 

Chapter IV 

Preliminary Analysis, Using Percentages and Association Coeffi- 
cients : 40 

Chapter V 
Final Analysis, Using Partial Correlations 68 

Chapter VI 
Summary and Conclusions 74 



PREFACE 

The most powerful tendency in education during the past 
two and one-half decades has been the development of a 
"body of quantitative technique which make constant use 
of statistical method" of study. The subjective is fast giv- 
ing way to the objective. Research in almost every line is 
being made to conform to the scientific method. There is 
still one phase of the work, however, in which some writers 
are seemingly content to make broad generalizing state- 
ments, often unsupported by scientific facts. 1 The prob- 
lem referred to is that of the relation of physical defects to 
progress in school. Who can explain why this, one of the 
most vital of all school problems, should be among the last 
to yield itself to modern methods of scientific study — one 
of the last to be subjected to the searchlight of scientific 
truth? All kinds of notions still prevail. 2 Who has not 
heard the "untutored" would-be sage proclaim that "suc- 
ceeding generations grow weaker as they grow wiser?" 
How does he know? Does nature compensate for physical 
incapacity with mental alertness? The truth of the mat- 
ter is that some relation between these attributes has been 
suspected, and, in the absence of supporting facts, these 
broad generalizations have been indulged in. 

Such differences of opinion as that referred to above is 
not uncommon. Diametrically opposite views are some- 
times held by prominent writers.-' How can agreement be 
brought about? It can be done only when facts are made 
to speak louder than theory. Ayres, together with a few 
others, a few years ago took the lead in a movement to put 
the whole discussion on an objective basis, with the effect 
that at present quite a bit of the literature on the subject 
shows signs of a change toward a scientific attitude. This 
is the more important when the fact is faced that medical 
and physical examinations are becoming the rule rather 

Reference is made here to such statements as that of Frank Allpors, M.D., Chair- 
man of Committee on Conservation of Vision, Chicago, in his pamphlet entitled 
'■School Children's Eyes," in which he says: "At least 5,000,000 of these children suf- 
fer from eye diseases or defects which seriously impair their school progress." Nei- 
ther Ayres nor Cornell found this statement concerning eyes supported by their data 
on promotion. Medical Inspection of Schools, page 202, Gulick and Ayres. 

-Cornell, W. S., Psychological Clinic, November 15, 1909. 

:, Albert E. Taussig. M.D., Clinic for St. Louis County, Mo., in Psychological Clinic, 
November 15, 1909, makes the following statement : "In the first place, there is no 
agreement as to what constitutes defective vision. In some cities everything less than 
perfect is reported. Elsewhere vision by both eyes must be less than perfect or must 
even be less than 20/30. 

Gulick and Ayres make the following statement in Medical inspection of Schools, 
page 82 : "Bayonne reports 7.7 r '< defective vision, while the congested districts of 
Cleveland report 71.7%. Of course such variations as this at once suggest what is un- 
doubtedly the case, that the results are largely influenced by the methods employed." 



6 Preface 

than the exception in our large cities and in many of our 
smaller ones. However, it is true that little use is being 
made of the great mass of information obtained from these 
examinations. 

Just what is the effect of physical abnormality on school 
progress? No one can be quite sure. It is hoped that this 
study will at least indicate the method to be used in finding 
out. It will emphasize the importance of scientific analy- 
sis of these complex relations. Though largely mathemat- 
ical, a fact for which no apology is offered, the treatment 
is less technical than might at first be supposed. In gen- 
eral, the plan of treatment begun by Ayres is followed, but 
with a much larger emphasis on the mathematical treat- 
ment of attributes. An attempt has been made to simplify 
the whole process to the extent of making it readable to a 
person of reasonable mathematical ability. A knowledge 
of simple association percentages and of correlation coeffi- 
cients is assumed. 

It is believed that the method here used is capable of 
fruitful applications to educational fields. Students of 
sociology have long made wide use of Pearson's association 
formulae. Cannot the field of school administration profit 
greatly from the development and application of a similar 
technique? 

No claim in this thesis is made to finality either in tech- 
nique or results. It is only a beginning. May not others 
be expected to take up the work thus begun and give it a 
more extended application in wider fields? That is the 
hope of the writer. 



INTRODUCTION 

historical background for present-day move- 
ments in health supervision 

The Movement in Foreign Countries 

Like a great many American institutions, this movement 
started in Europe. 1 It was almost half of a century after 
the French began to examine school children before it was 
undertaken in American schools. 2 Early records mention 
medical inspection in Paris as early as 1833, though the 
first real inspection in Paris was begun in 1874. A more 
noteworthy event was the establishing of a comprehensive 
system of medical supervision in Brussels, Belgium, 1774. 
Regular physicians were employed to visit all the schools 
three times per month. This plan attracted so much atten- 
tion that Antwerp, Louvain, Liege, and other cities almost 
immediately took up the movement. The Swiss were the 
next to borrow the Belgian idea. The Germans do not 
claim to have gotten their scheme from the Belgians, as 
some sort of eye examination had been in practice in Dres- 
den three years prior to the Brussels movement. But the 
facts are that the first real comprehensive system of phys- 
ical examination in Germany was begun in Wiesbaden in 
1889. This last date proved to be a landmark in the history 
of inspection. This type of inspection, which included a 
thorough examination of the heart, lungs, throat, spine, 
skin, and the higher sense organs, has been widely adopted 
throughout Europe. The child was examined on entering 
school for the first time and reexamined each third year 
thereafter. This was in addition to the usual routine of 
medical inspection. 

The other continental countries to fall in line were Hun- 
gary, 1878 ; Norway, 1889, a system of three examinations 
per year ; Sweden, 1878, a system of annual examinations ; 
Roumania, 1899, annual examinations; Moscow, 1895, a 
system comprising six physicians in charge of the seventy- 
two elementary schools. 

England, like her American offspring, was rather tardy 
in contributing her share to the movement. It was not 
until 1908 that she could claim a real system of examina- 
tions. This was the year of the beginning of the national 
"Society of Medical Officers," an organization formed for 
the purpose of putting the movement over. Her sudden 

•Gulick and Ayres, Medical Inspection of Schools, Chap. III. 
-Bureau of Education Bulletin, 1919. No. 4. 



8 Introduction 

and fitful sprint, coming late as it did, was probably due in 
part to the influence of her French neighbors. This same 
year marks the beginning in France of the "La Medecine 
Scholaire," a monthly bulletin published by the "Society 
for the Inspection of Schools." It was evidently this last- 
named society that had much to do with the creation of a 
similar one in England. 

Other countries outside of Europe had made progress in 
medical and physical inspection. Egypt had had a com- 
prehensive system, with highly paid inspectors, since 1882 j 1 
Chile, since 1888 ; Japan, since 1898 ; and America, since 
1892. To the last-mentioned we will now turn for further 
historical development. 

The Movement in America 

As stated above, medical inspection did not begin in 
America until about the beginning of the last decade of the 
nineteenth century. The movement is generally thought to 
have begun in New York, under the leadership of Dr. 
Morse, about 1892. This is disputed, however, by good 
authority. 2 According to this authority, the first system 
in America was inaugurated in San Antonio in 1890. It 
is not material which of these claims is correct; for, with- 
out question, the first permanent scheme was inaugurated 
in Boston in 1894, with a corps of fifty inspectors — one for 
each of the fifty districts. Chicago introduced a similar 
system in 1895, with nine physicians. From this time on 
other cities followed in rapid succession until prior to the 
Great War there were more than seventy cities maintaining 
some kind of physical examinations. This did not include 
the thirty-two cities and three hundred and twenty-one 
towns of Massachusetts. This state, together with six oth- 
ers, had compulsory state-wide medical inspection. The 
other six were Connecticut, New Jersey, Vermont, New 
York, Utah, and California. The impetus given physical 
training during the Great War, 1 together with the amazing 
revelations made by the Draft Board concerning our phys- 
ical unfitness as a nation, caused school authorities, both 
state and local, to speed up legislation pertaining to elimi- 
nation of physical defects and the prevention of disease. 
The result is that at present every state in the Union main- 
tains some kind of inspection, the same being a specific 
requirement of law in all except a very few states. 2 

^Gralick and Ayres, Medical Inspection of Schools, page 23. 
-Bureau of Education Bulletin, 1919, No. 13, page 28. 
^Bureau of Education Bulletin, 1919, No. 4. 
^Bureau of Education Bulletin, 1919, No. 13, page 28. 



Introduction 9 

In 1917 the following laws were passed: 1 New Hamp- 
shire, requiring schools to vote on the question of inspec- 
tion ; Nevada, providing for examination of the eyes, ears, 
teeth, and mode of breathing; North Carolina and North 
Dakota, providing for examination by county authorities ; 
Pennsylvania, providing for the treatment of the eyes and 
teeth ; New Jersey, requiring dental clinic ; Rhode Island, 
requiring treatment of the teeth ; and Virginia, authorizing 
the county board to expend funds in providing inspectors 
and nurses to visit the schools. These illustrate the tenden- 
cies in legislation most prominent then and the ones that 
have persisted to the present time. 

A summary of the legislation of 1918-1919- is also sig- 
nificant. Twenty-eight states either amended old laws or 
passed new ones. Six of these — New Jersey, California, 
Connecticut, Kansas, Nebraska, and North Carolina — spec- 
ify the treatment of defectives. The others either do not 
specify at all or specify medical inspection. The distribu- 
tion is as follows : 

Unspecified defects — North Carolina 1 

Treatment of ears — South Dakota, Nebraska 2 

Treatment of eyes — South Dakota, Nebraska, California 3 

Treatment of nose — South Dakota 1 

Treatment of throat — South Dakota 1 

Mode of breathing — Nebraska 1 

Providing for clinic for examination of teeth — New Jersey, Ohio, 

South Dakota, California, Connecticut, Kansas, Nebraska 7 

Total 16 

If this table seems to put most stress on teeth, eyes, and 
ears in the order named, it is probably due to the fact that 
it is not known to what extent the other twenty-one states 
passing laws this same year included only these three in 
their program of general inspection. 

Attention has already been called to the fact that often 
no distinction is made between physical examination for de- 
fects and medical inspection. There is a difference, and 
there should be a distinction. The difference lies chiefly in 
the fact that medical inspection deals primarily with pro- 
tective measures looking to the safeguarding of the com- 
munity against contagious diseases. This is immediate pro- 
tection against present dangers. Physical examinations 
are more constructive in their aim, having for their object 
the detection of defects that prevent the proper develop- 
ment of our coming generation and, so far as possible, elimi- 
nation of these defects. The latter is the most profitable 

1 Bureau of Education Bulletin, 1919, No. 13, page 28. 
'Bureau of Education Bulletin, 1920. Ed. Legislation. 



10 Introduction 

form of inspection, but is the form that has at times re- 
ceived least attention. Ayres says in his Laggards in Our 
Schools that a thorough examination of all the pupils is 
rare. The laws cited above indicate that the tendency is 
more inclined toward a constructive program of physical 
examinations. 

There is some difficulty at present, however, in that there 
are no very reliable standards. 1 There is also noticeable 
lack of understanding regarding the technique of the ex- 
aminations. The specific defects are not sufficiently defined. 
Different examiners vary widely in what is considered a 
defective. The result is that the data obtained from dif- 
ferent surveys are not comparable and are often meaning- 
less to persons not familiar with the method used. Uni- 
formity of method, producing comparable results, must be 
brought about before the greatest good can come from this 
kind of work. 



1 Cornell says : "As a consequence, enormous figures may be quoted which are im- 
pressive enough, but which fail to add to our medical knowledge. ... As a mat- 
ter of fact, they have occasionally done harm by reason of their employment as a basis 
for deduction as to the degeneracy of the race, the relation of physical to mental 
defects. — Psychological Clinic, November 15, 1909, page 160. 



CHAPTER I 
PREVIOUS OBJECTIVE STUDIES OF RELATED SUBJECTS 

Prior to the introduction of standard achievement tests, 
an objective study of the relation of physical well-being to 
achievements was next to impossible. This, doubtless, is 
the explanation for the fact that so little attention has been 
given this phase of school administration. Research men 
have been satisfied with collecting physical data, tabulating 
them, and stating the relative percentages of defectives. 
Most of the state and city surveys of physical defects of 
school children have been of this type. While there has 
been no study made from the standpoint of standard tests, 
a few related studies have been made. 

Among the men that have attempted an objective treat- 
ment of the relation of physical defects to achievements 
are Dr. Walter S. Cornell and Dr. S. W. Newmayer, in Phil- 
adelphia; 1 Superintendent James E. Bryan, of Camden, 
N. J. ; 2 a little more recently, Luther H. Gulick and Leon- 
ard P. Ayres, in New York ;•'• and still more recently, Brad- 
ley Ruml et al., 4 who have recently printed a psycho-phys- 
ical study, which resembles somewhat, though not in details, 
this study. Each of these studies will be briefly reviewed 
before taking up the present problem. 

Defects Among "Exempt" and "Nonexempt" Children. — 
This study was made by Dr. Cornell 5 on a small group of 
children (219) from six to twelve years of age in one school 
in Philadelphia. He is among the early writers to under- 
take the objective treatment of this subject. He studied 
marks made by defective and "normal" children. 

Average Per Cent 
in Studies 

Normal children 75 

Average children 74 

General defectives 72.6 

Children with adenoids and enlarged tonsils 72 

In another school he examined 907 children and classi- 
fied them on the basis of "exempt" and "nonexempt." 

^■Psychological Clinic, January, 1908. 

= Quoted from "Laggards in Our Schools," Ayres. 

3 Medical Inspection of Schools, Gulick and Ayres. 

*Methods and Results of Testing School Children, Dewey, Child, Ruml ; E. P. Dut- 
ton & Co., New York. 

5 Dr. Walter S. Cornell, of the Medical Department of the University of Pennsyl- 
vania. For the original report, see Psychological Clinic of January 15, 1908. For 
extract of same, see Gulick and Ayres. Medical Inspection of Schools, page 189. 



Geography 


Spelling 


Average 


69 


76 


75— 


71 


77 


73+ 


70 


71 


69 



12 A Study of the Relation of Some Physical Defects 

Exempt Nonexempt 

Children examined 907 687 

Per cent defective 28.8 38.1 

In another school he classified as "bright," "dull," and 
"dullest" 150 children, as follows : 

Bright Dull Dullest 

Children Children Children 

Number examined 89 32 29 

Having nose or throat defects 16 9 9 

Per cent 11.1 28.1 31 

In another report 1 he gives percentage marks made in 
school subjects, the children being classified on the basis of 
"normal," "fair," and "bad" vision. 

Children With — Arithmetic 

Normal vision 79 

Fair vision 70 

Bad vision 66 

These percentages were based on teachers' marks, and 
not upon results from objective tests, as this study was 
made before the introduction of tests in the school work. 
They are as reliable as could be obtained at that time on 
individual achievement. The groups were small, and are 
valuable chiefly for the fact that they indicated the prob- 
able truth of some association between physical defects 
and progress and led to further study. Cornell concludes 
that educational results in our schools suffer a discount of 
about six per cent in the case of physically defective chil- 
dren — this conclusion, of course, being based upon teachers' 
marks, as stated above. He points out also that much time 
rightfully belonging to the normal children is wasted. 

Cause of Backwardness in Camden Schools. — This inves- 
tigation was made by James E. Bryan, and included 10,130 
children. From these, 2,020 children of excessive age were 
selected. He considered a child overage if he were one 
year or more behind his grade (compared with usually ac- 
cepted standards). These were distributed according to 
cause of overageness into seven groups. 

Excessive Age Due to — Defects 

Other Than 
Sight and Mental 
No. Age Upon Hear- Weak- 

Exam. Starting Absence Slowness Dullness Health ing ness 

Per Cent Per Cent Per Cent Per Cent Per Cent Per Cent Per Cent 

Boys 1,081 20.2 29.4 19.8 12.1 7.4 3.6 4.6 

Girls 939 22.4 27.5 22.4 11.9 12.1 4.4 2.6 

Total 2,020 21.2 28.5 21.0 12.0 9.6 3.9 3.7 



^New York Medical Journal of June 1. 1907. 



to Achievement in the Elementary School 13 

He concludes that physical defects constitute a cause, but 
not the cause, of retardation ; secondly, that the bearing of 
physical defectiveness on school backwardness does not ap- 
pear to be very great. 

Physical defects other than sight and hearing were as- 
signed as reasons for excessive age in 3.6 per cent of the 
cases of the boys and 4.4 per cent of those of the girls. 

Laggards in Our Schools. 1 — This book was first printed in 
1908. Its purpose was to throw some light on the subject 
of retardation. Among the causes, defects is given a prom- 
inent place, though only fourteen pages of the book are 
devoted to this subject. Ayres made a study of 3,304 chil- 
dren in New York City from the standpoint of the influence 
of defects on promotion. There were no standard tests at 
that time, so he was forced to judge school progress in 
terms of teachers' estimates and promotions. In substance, 
his findings are set forth in the following tables : 

Table 68 — Per Cent of Dull, Normal, and Bright Pupils Suffering 
from Each Sort of Defect. Ages, Ten to Fourteen, Inclusive. All 
grades. 

Dull Normal Bright 

Defects Per Cent Per Cent Per Cent 

Enlarged glands 20 13 6 

Defective vision 24 25 29 

Defective breathing ■ 15 11 9 

Defective teeth 42 40 34 

Hypertrophied tonsils 26 19 12 

Adenoids 15 10 6 

Other defects 21 11 11 

Number examined 407 2,588 309 

Defects per child 1.65 1.3 1.07 

Per cent not defective 25 27 32 

Per cent defective 75 73 68 

Table 70 — Showi?ig Per Cent of Loss in Progress of Children Suffer- 
ing from Each Sort of Physical Defect. 

Per Cent of Loss 
Kinds of Defects in Progress 

Enlarged glands 14.9 

Defective vision None 

Defective breathing 7.2 

Defective teeth 5.9 

Hypertrophied tonsils 8.9 

Adenoids 14.1 

Other defects 8.5 

Average 8.8 

From Table 68 Ayres concludes that "in every case, ex- 
cept in that of vision, the children rated as 'dull' are found 
to be suffering from physical defects to a greater degree 

Leonard P. Ayres, now president of Cleveland Trust Company, Cleveland, O., for- 
merly with Russell Sage Foundation. 



14 A Study of the Relation of Some Physical Defects 

than the normal or bright children. It is true that 75 per 
cent of the dull children are defective, as compared with 
73 per cent among the normal and 68 per cent among the 
bright children." He says further: "The differences are 
slight. But the defective dull child has, on the average, 
1.65 defects, as against 1.07 for the bright one. In other 
words, the number of defectives among the dull children 
does not differ widely from the number of defectives among 
the bright ones ; but the dull child is found to be much more 
defective in degree." 

From Table 70 Ayres draws his conclusions as to the seri- 
ousness of the handicaps in terms of percentages. For in- 
stance, he concludes that children suffering from physical 
defects made, on the whole, 8.8 per cent less progress than 
did those having no physical defects. 

In his Table 67, which is not shown here for lack of space, 
he shows data from which he concludes that physical defects 
decrease with age. He briefly summarizes as follows : 

1. "Physical defects decrease with age." 

2. "It has been shown that vision does not follow the 
same rules as do the other defects." 

3. The examinations conducted in New York have shown 
higher percentages of enlarged glands, defective breathing, 
hypertrophied tonsils, and adenoids among dull children 
than among the bright children. 

4. It has been demonstrated that physical defectiveness 
has a distinct and important bearing on the progress of 
children. 

Medical Inspection of Schools (Gulick* and Ayres). — This 
entire book is given to medical inspection and physical ex- 
aminations ; but only Chapters VII, which deals with "Phys- 
ical Examinations for the Detection of Noncontagious De- 
fects," and XII, which discusses "Retardation and Physical 
Defects," are directly related to any part of this study. 
The first-mentioned chapter deserves notice from the fact 
that two instructive tables are given — one showing per cent 
of vision and hearing defectives in fourteen countries, coun- 
ties, and cities for the. sake of comparison, the other show- 
ing the percentage distribution of defects for New York 
and Minneapolis. The last table is quoted below : 

1 Director of Physical Training, New York Public Schools. 



to Achievement in the Elementary School 15 

Table (K) — Physical Examinations in the New York and Minneap- 
olis 1 Schools. 

Nei» York, Minneapolis, 

1906 Per Cent 1908 Per Cent 

Number examined 78,401 100 710 100 

Bad nutrition 4,921 6.3 166 23.3 

Anterior cervical glands _-_29,177 37.2 377 53.0 

Posterior cervical glands 8,664 11.0 

Chorea 1,380 1.7 2 0.2 

Cardiac disease 1,096 1.4 15 2.1 

Pulmonary diseases 757 .9 30 4.2 

Skin diseases 1,558 1.9 12 1.6 

Deformity of spine 424 .5 

Deformity of chest 261 .3 

Deformity of extremities 550 .7 

Defective vision 17,928 22.8 170 23.9 

Defective hearing 869 1.1 55 7.7 

Defective nasal breathing__ll,314 14.4 

Defective teeth 29,597 55.0 309 43.5 

Defective palate 831 1.0 2 0.2 

Hypertrophied tonsils 18,306 23.3 221 31.1 

Postnasal growth 9,438 12.0 91 12.8 

Defective mentality 1,857 2.3 

Where treatment was nec- 

sary 56,259 71.7 462 65.1 

It will be observed that there are wide differences in the 
percentages for the two cities. Ayres attributes most of 
this to the difference in rigidity of examination. He re- 
marks, however, that the most interesting figures of all are 
those for "where treatment is necessary." "These per- 
centages are 71.1 for New York and 65.1 for Minneapolis." 

Chapter XII, 2 mentioned above, deals largely with the 
distribution of defects which on the whole decrease with age. 
He makes the statement also that from 100,000 cases ex- 
amined among school children it has been found that from 
66 to 72 per cent are defective. This agrees very closely 
with the findings in this study, where 64 per cent were 
found sufficiently defective to need treatment. Of the many 
tables given, only one will be quoted here as being different 
from any mentioned above. 

Table (Y) — Per Cent Having Each Defect by Sexes. 

Boys Girls 

Defectives 78.5 79.2 

Enlarged glands 32.2 20.3 

Defective vision 15.7 20.8 

Defective breathing 19.1 14.3 

Defective teeth 48.4 53.5 

Hypertrophied tonsils 33.1 24.7 

Adenoids 17.4 15.6 

Other defects 13.6 14.7 



^Medical Inspection of Schools, page X~. 

-The data in this chapter were secured in the Manhattan Schools during Mav and 
June, 1908. 



16 A Study of the Relation of Some Physical Defects 

Table (Y) is interesting, inasmuch as it compares "per 
cent defective" among boys and girls. From the examina- 
tion of 3,301 boys and 4,305 girls, the boys were found to be 
defective oftener than the girls with respect to enlarged 
glands, defective breathing, and hypertrophied tonsils; 
while the girls were oftener defective with respect to vision 
and teeth. The latter happen to be the ones that Ayres 
finds least apt to cause retardation. 1 This should mean 
that boys, as a rule, are more retarded, other things being- 
equal, than girls. As stated below, Ruml is planning to 
make further study of this phase of the problem. 

Chief among the conclusions reached by Gulick and Ayres 
in this study is, quoting from them: "Physical defects con- 
stitute a cause, not the cause, of retardation." 

A study was made in" New York City in 1915 by Evelyn 
Dewey, Emily Child, and Beardley Ruml for the purpose 
of obtaining norms for a series of tests as a basis for further 
study of the value of mental tests for improvement of 
schoolroom procedure. The printed report of the study 
naturally divides itself into two large divisions — the method 
used in collecting the data and the methods used in their 
interpretation. Ruml leaves most of the interpretation for 
a second volume yet to appear in print. The thing that is 
of interest in this connection about the first volume is the 
fact that the relations between test scores and attributes are 
touched on, though they are not treated by Pearson's for- 
mulae. 

The tests were given to 3,000 Jewish children between 
the ages of eight and thirteen, most of whom were found in 
a single school in New York City. Jewish children were 
selected because of their race homogeneity. The influence 
of race characteristics could then be eliminated from the 
study. The tests given were Whipple's: grip, steadiness, 
tapping, rote memory, sentence completion, cancellation of 
A's, association of opposites, substitution, card sorting 
(Jastrow), and certain other tests, as nail driving, needle 
threading, fastening buttons, cart construction, narrative 
pictures, and instruction box. Each child was given a sep- 
arate examination and had from twenty-five to forty-five 
minutes on each question. The data were grouped accord- 
ing to the ages of the children. The mean, standard devia- 
tion, and regression of score on age were found. The table 
below will illustrate: 



^t was pointed out above that James Bryan in the Camden investigation found 
that physical defect was the cause of average in 4.4 of the cases among the girls and 
in only 3.6 per cent of cases among the boys. It is difficult to harmonize these two 
conclusions. The difference may be due to local conditions in New York and Camden. 



to Achievement in- the Elementary School 17 

Picture Completion Index 

Age 9-9.9 10-10.9 11-11.9 12-12.9 13-13.9 

Mean 12 ± .11 56.7 ± .36 19.1 ± .39 24.6 ± .22 25 6 .18 

S. D. 54 ± .02 .59 ± .02 .50 ± .02 .53 ± .02 .53 .02 

Regression equation: 9.49 .183 age Sig. = .564 

Tables of this kind were worked out for each test, boys 
and girls separately. Deviations for each sex of several 
ages were found. These were used as the bases for deter- 
mining the influence of sex, maturity, etc., on scores. The 
standard deviations of the small groups were subtracted to 
find by what amount they differed. This difference was 
divided by the probable error of the difference. If this dif- 
ference were less than the probable error, it was disre- 
garded. If it were from one to three probable errors, it 
was of "possible" significance. If it were more than three 
times the probable error, it was of "probable" significance. 
From these probable error differences Ruml concluded that 
boys were stronger in picture completion. In fact, he con- 
cluded that girls excel only in needle threading and in 
steadiness. The standard deviations in the picture com- 
pletion tests are given here for comparison : 

Picture Completion Index 

Age 9-9.9 10-10.9 11-11.9 12-12.9 13-13.9 

Boys, S. D .52 .59 .50 .53 .53 

Girls, S. D .33 .43 .38 .43 .41 

In each of these age groups the boys seem to show a 
larger deviation, and there is an evident difference; but as 
the probable error of the differences is not shown in the 
table, the extent of difference cannot be indicated here. It 
would be interesting to have the original data from which 
to work out the association coefficients according to the 
Pearson formulae. 

The data mentioned above do not touch upon physical 
defects. This is to be regretted, inasmuch as the physical 
data constitute the portion of Ruml's study which comes 
closest to the problem being worked out in this study. But 
as this part of it is not yet in print, except the tabulated 
data, it can only be surmised as to the method to be used 
in its interpretation. The usual physical examinations 
were given, except that no notice was taken of defects of 
the eyes, ears, nose, and throat. In fact, the only defects 
reported that are included in this study are the defects of 
the teeth. The data collected had to do with heights, 
weights, blood pressure, etc. It was tabulated and the 
means, standard deviations, and probable errors found as 



18 A Study of the Relation of Some Physical Defects 

in the tests above. It is presumed that the standard devi- 
ation method of comparison is to be used in its interpreta- 
tion as with the other data. The deviations by ages and 
sex are shown below for the number of permanent teeth : 

Number of Permanent Teeth 

Age 9-9.9 

Boys, S. D 1.08 .08 

Girls, S. D 2.87 .20 

It will be noticed that, with the exception of the first and 
fourth groups, the boys have larger standard deviations; 
but this may not be significant, as the standard deviations 
for the entire sex groups are not given. 



10-10.9 


11-11.9 


12-12.9 


13-13.9 


3.81 .26 


4.05 .34 


2.25 .16 


1.94 .13 


3.73 .26 


3.07 .21 


2.86 .19 


1.30 .09 



CHAPTER II 
THE PURPOSE AND SCOPE OF THE PRESENT STUDY 

The purpose of the study is clearly expressed in the state- 
ment of the problem. It reads : "A Study of the Relation 
of Some Physical Defects to Achievement in the Elementary 
Schools." It is difficult to state a research problem of this 
kind clearly enough to be understood alike by all. Few 
statements are so perfect that they cannot be distorted. 
Too much may be read into them, or too little. A prob- 
lem should be so defined as to include the essentials of a 
unified study and to exclude the nonessentials. Depth is 
often more to be desired than breadth. An attempt has 
been made to narrow the present study down to the single 
purpose of arriving at the degree of association, if any, be- 
tween physical defects and achievements in the elementary 
schools. The fact that this study is based on standard test 
scores and physical examination restricts it to the objective. 
"Hearsay" and teachers' estimates give way to quantita- 
tive study and objective measurements. Scores come under 
the head of variables and physical examinations under at- 
tributes. Either of these yield themselves readily to math- 
ematical treatment. This, in fact, is the method used to a 
very large extent in this study. Whenever it was possible 
to use mathematical formulae to aid in the interpretation 
of the data, they have been so used. 

It is believed that the contributions made by the present 
study to education are threefold. 

1. The study calls attention to a wide field of research 
dealing with the relation of physical defects to achievement 
scores. Being one of the first to deal with achievements 
in this way, it should influence others to take up the work 
and to make more extended studies. 

2. The study indicates the methods for applying the the- 
ory and formulae of attributes to problems of school ad- 
ministration, many of which cannot be studied directly from 
the standpoint of variables. Attributes have for quite a 
while had a very prominent place in the study of sociology. 
This is an attempt to use similar methods in the field of 
education. Indeed, a large part of that technique has been 
brought over into this new field. 

3. So far as it is possible to base conclusion on the results 
of a single piece of research, this study indicates the rela- 
tion of physical defects to achievement scores. 

It is well to state, in the outset, that this study does not 



20 A Study of the Relation of Some Physical Defects 

undertake to trace the probable effects of physical abnor- 
malities on mental ability. Intelligence comes into consid- 
eration only as a factor influencing association of defects 
with achievement scores. This discussion, for this reason, 
keeps off the psychological processes underlying the learn- 
ing process — not that such a study would not be interesting 
and profitable, but because such a discussion belongs to the 
field of psychology. The real problem here is the relation 
of physical defects to achievement scores as shown by stand- 
ard tests. Neither is this study concerned with the under- 
lying biological factors, such as heredity and environment, 
that, without doubt, affect school progress. The consider- 
ation of these would lead too far afield. Home environment 
and its relation to standard scores would of itself make a 
subject of much interest, and sufficiently complex for a 
thesis. 

It will be observed also that "some" of the physical de- 
fects are to be studied. A consideration of the whole cate- 
gory would be too extended and not so profitable as a more 
detailed study of the most prominent ones, which include 
defects of eyes, nose, throat, tonsils, and teeth. Ninety-five 
per cent of all defects reported in this study come under 
these five heads. This is further discussed in connection 
with Table II. The ones not specifically considered have 
been noted, however, and disposition made of them in a way 
not to invalidate the present study. 

This study has undertaken to show, first, the apparent 
relations as indicated by percentages and as indicated by 
association coefficients derived from fourfold and manifold 
formulae, without considering the effect of other factors, 
such as intelligence ; and, second, the same coefficients after 
being freed, by the use of partial correlations, from the 
influences of these other factors. An example here will 
suffice for the present, as a full discussion of this phase is 
included in Chapter III. 

It will be shown later, in Table LII, that the coefficient 
of association between defective tonsils and spelling achieve- 
ment scores is .084. This means that in this school if a 
child with defective tonsils is selected at random, the 
chances are slightly in favor of his having low achievement 
scores. But is this association of defective tonsils with 
scores in spelling direct, or is it due to the connection that 
both defective tonsils and scores in spelling have with gen- 
eral intelligence? After the association has been freed 
from the influence of intelligence, the coefficient is .08. 
This result is not very different from the .084 first obtained, 



to Achievement in the Elementary School 21 

but shows that the influence of defective tonsils is slightly 
less than was first supposed. 

These original coefficients and those derived from partial 
correlations are found not only in respect to the general 
problem — that is, the relation of defects in general to 
achievements in general — but the effect of specific defects 
on the general achievement, as well as specific defects on 
individual subjects, such as reading. The results of these 
comparisons are stated in Chapters IV and V and summa- 
rized in Chapter VI. 



CHAPTER III 

MATERIAL AND METHODS USED IN THIS STUDY 

The data used in this study were secured by means of a 
survey of the elementary grades in the public school of the 
town of Humboldt, Tenn. 1 This survey included the giv- 
ing of standard tests to all the pupils up to and including 
the eighth grade and giving each child a thorough physical 
examination. The physical examination was in charge of 
Miss Sanborn, 2 a registered health nurse. The achieve- 
ment tests consisted of a series of tests covering all the ele- 
mentary school branches. The tests selected for this pur- 
pose were arithmetic, Monroe and the Cleveland ; spelling, 
Buckingham Extension of the Ayres' Scale; geography, 
Hahn Lackey; writing, Freeman Scale; reading, Monroe 
Silent Reading; English, Trabue Extension and Nassau 
County Supplement of Hillegas Scales. 

The Illinois intelligence test was given all grades above 
the second. Holley's picture tests were used in the first 
and second grades. 

For the most part, the papers were scored by the direc- 
tors of the survey. The scores were tabulated by classes 
and the medians determined. The latter were used in de- 
riving the percentage score shown in Table I. The details 
of that process are explained in connection with the inter- 
pretation of that table. As explained below, this procedure 
made it possible to combine scores made by a child in vari- 
ous subjects and also to combine like subjects throughout 
the elementary school. The method of averages used is also 
explained in the proper place below. It is sufficient here 
simply to say that the median per cent score was taken as 
the average achievement for each child. 

x The survey was directed by J. N. Mallory, Superintendent of Student Activities, 
Union University, Jackson, Tenn., and L. D. Rutledge, Professor of Education in the 
same school. 

-Miss Sanborn is a graduate of a nurse training school, served overseas during the 
war, and is now regularly employed by the Red Cross and is stationed at Humboldt. 



to Achievement in the Elementary School 



23 



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24 A Study of the Relation of Some Physical Defects 

Explanation of Table I. — This table includes only the 
first six pupils of one section of the third grade, only enough 
of the original data being given here to illustrate the method 
of refining and interpreting the data. The figures in the 
first column represent the names of pupils; those in the 
second, the ages ; the third, intelligence score ; the fourth, 
the intelligence score reduced to per cent of the median for 
the class ; the odd columns from 5 to 15, scores in the re- 
spective subjects; the even columns from 6 to 16, the per 
cent of median for the respective subjects ; column 17, 
medians of per cents of median for each pupil ; and columns 
18 to 21, defects. Some method of combining the achieve- 
ment scores made by each child in the various subjects in 
order to arrive at a measure of his general ability was to 
be found. Any method of doing this would require that all 
these achievement scores be reduced to a common unit. 
The simplest method of doing this is to reduce each score to 
per cent of the median for the class in the respective sub- 
jects, as is done in the table, and then take the average to 
represent general ability. This method of combining scores 
is the one used by Dr. Joseph Peterson, of Peabody College, 
in the Paducah Survey, and recommended by him in his 
article in the Journal of Educational Research for April, 
1921. The method has been used in this study in prefer- 
ence to the more complicated method of standard devia- 
tions. To get the per cent score, the original score was 
divided by the class median which is shown at the bottom 
of each column. The first score in column 5 under writing 
is 7. When 7 is divided by 9.25, the median shown at the 
bottom of this column, the 76 shown in column 6 is ob- 
tained as the corresponding per cent score. In the same 
manner the figures 111, 52, 80, 112, 75, and 195 in the first 
'row were obtained. The 111 is the per cent intelligence 
score, and is not combined with the others in getting the 
average, as it is treated as a separate factor and is used as 
such in the study of relations in Chapter V. The ones to 
be used, therefore, in the average are 76, 52, 80, 112, 75, 
and 195. The median 1 of the row falls halfway between 
76 and 80, or on 78. If the second row be taken, the per 
cent scores are 86, 56, 80, 112, 105, and 61. Here the 
median falls halfway between 80 and 86, or on 83. 

Restating what has been said above, the entire first row 
may be read as follows: Pupil "1" is 9 years of age; his 
scores are 25, 7, 5, 14, 54, 5, and 32 in intelligence, writing, 
language, spelling, reading rate, reading comprehension, 
and arithmetic, respectively ; his per cent scores are 111, 

x The median was selected as the average in preference to the mean because of. the 
mathematical objection to using the mean with so few cases (six in this class). 



to Achievement in the Elementary School 25 

76, 52, 30, 112, 75, and 195 in the subjects in the order just 
named ; his median of per cents is 78 ; and he has defective 
vision. The last fact is indicated by the check "1" under 
vision in column 20. 

Physical Defects. — Every precaution was taken to make 
the data derived from the physical examinations reliable. 
Miss Sanborn spent almost the whole of a school month in 
this work. Each child was examined privately and with 
painstaking precision. 

It is true, however, that only such defects as could be 
detected without the use of the X-ray and other expensive 
apparatus were reported. The results as reported by Miss 
Sanborn are tabulated in Tables II and III. 

Explanation of Table II. — This table is intended to show 
the total number of defectives in the eight grades, and to 
show how these were distributed. The Roman numerals 
in column I indicate the grades. The Arabics in the other 
columns indicate the frequencies. Across the top the data 
read: In the first grade there were 34 boys and 43 girls, 
of which 26 boys and 20 girls were without defects, while 
17 boys and 14 girls had defects. That is to say that 31/77 
of the first grade had such defects. The other rows are 
read in the same manner. Reading the last row, it is found 
that of the 515 pupils examined, 245 were boys and 270 
were girls ; 61 boys and 103 girls had no defects, while 331 — 
164 boys and 167 girls — had defects. It will be seen that 









TABLE ] 


[I 












Defectives 


BY 


Grades 








No. 


Examined 


Without Deff.cts 


Wit 


h Defects 


Grades 


Boys 


Girls 


Total 


Boys 


Girls 


Total 


Boys 


Girls Total 


I 


. 43 


34 


77 


26 


20 


46 


17 


14 31 


II 


40 


32 


72 


20 


20 


40 


20 


12 32 


III 


29 


43 


72 


11 


16 


27 


18 


27 45 


IV 


28 


23 


51 


9 


5 


14 


19 


18 37 


V 


22 


30 


52 


3 


13 


16 


19 


17 36 


VI 


20 


17 


37 


5 


7 


12 


15 


10 25 


VII 


22 


35 


57 


1 


6 


7 


21 


29 50 


VIII 


21 


41 


62 


5 


11 


16 


16 


30 46 



Mixed 18 17 35 15 6 17 12 29 

Totals 243 272 515 81 103 184 162 169 331 

331 515 of the total number examined were defective. 
This is a little more than 60 per cent. Everything that was 
thought to be serious enough to require treatment was re- 
ported. This included the five major defects — eyes, ton- 
sils, nose, teeth, and hearing — and, in addition, twenty-one 
of the less frequent ailments. The twenty-one cases were 
distributed about equally among goitre, undernourishment, 



26 A Study of the Relation of Some Physical Defects 

undersize, breathing trouble besides obstructed nasal cavi- 
ties, throat trouble other than tonsilitis, and deformed 
limbs. 

These twenty-one cases were found to distribute them- 
selves so that 52 per cent of these defectives made less than 
100 per cent achievement score, while 48 per cent made 
above 100 per cent score. Because of this near fifty-fifty 
distribution, these minor ailments have been disregarded 
and the study confined to the five major defects (eyes and 
vision counted together as one) . 

Explanation of Table III. — This table is similar to the 
one above, except that it contains only those cases having 
defective tonsils, eyes (or vision), nasal cavities, teeth, and 
hearing. Reading the first two rows across the top, with 



TABLE III 

Distribution of Physical Defects by Grades and Ailments 



Defects 

Vision 

Eyes 

Hearing 

Nasal Obstruction 

Tonsils 

Teeth 

Totals 
Grand Total 



Boys 
Girls 
Boys 
Girls 
Boys 
Girls 
Boys 
Girls 



Grades 



Sex I 

Boys 5 

Girls 






1 
2 
1 
21 



III IV 
4 
6 3 







1 


1 

10 



To- 
VI VII VlII tals 

1 1 1 17 

2 5 7 34 



3 4 
9 12 



23 13 15 11 



1 
3 

4 
1 
3 
5 
4 
13 



7 
11 

8 
15 
14 
23 
73 
66 



Boys 
Girls 


8 
1 


7 
4 


11 
13 


10 

9 


14 
11 


24 

17 


17 
16 


14 
22 


102 

93 


Boys 
Girls 


35 
6 


15 
13 


24 
39 


20 
25 


34 
31 


43 

38 


30 
43 


18 
55 


219 
250 



41 28 63 45 65 81 73 73 U69 



bad vision in the first grade there are 5 boys and no girls ; 
in the second grade, 1 boy and 3 girls ; in the third grade, 
4 boys and 6 girls ; in the fourth grade, no boys and 3 girls ; 
in the fifth grade, 4 boys and 6 girls ; in the sixth grade, 1 
boy and 2 girls ; in the seventh grade, 1 boy and 5 girls ; in 
the eighth grade, 1 boy and 7 girls; total, 17 boys and 34 
girls. For the other defects the reading is similar. The 
last row gives the totals of grades as follows: first grade, 
35 boys and 6 girls ; second grade, 15 boys and 13 girls ; 

^his total should not agree with the total in Table II. The total in Table II is 
the number of defective children examined. The total, in Table III is the number of 
"defects." Some children had several defects. 



to Achievement in the Elementary School 27 

third grade, 24 boys and 39 girls ; fourth grade, 20 boys and 
25 girls ; fifth grade, 34 boys and 31 girls ; etc. The grand 
totals in the last row give the total number of pupils having 
these defects, boys and girls combined : first grade, 41 ; sec- 
ond grade, 28 ; third grade, 63 ; fourth grade, 45 ; etc. 

Justification of Data. — The nature of this study does not 
make it highly essential rigidly to prove that the group of 
students here studied presents a normal distribution. It 
is not necessary to apply the tests for soundness of random 
selection, for the reason that the consideration of the prob- 
lem from the standpoint of attributes only requires that in- 
vestigation be limited to a definite time, place, and material, 
or that the universe be determined. When the universe is 
once establishd, the only other condition to be satisfied is 
that the investigations go on under uniform conditions and 
requirements throughout. If the lines of class distinction 
are sufficiently defined to make classification certain, the 
relative ratios of frequencies is not material. Yule makes 
the following observation : 

"The student should note that the value of Q for a given 
table is unaltered by multiplying either a row or a column 
by any arbitrary number — i. e., the value is independent of 
the relative proportions of A's and a's included in the table. 
This property is important, and renders such a measure of 
association specially adapted to experiments in which the 
proportions are arbitrary." It is interesting to note, how- 
ever, that both the distribution of Illinois intelligence scores 
and diseases show the group to conform rather closely to 
the normal expectation for the country at large. 

Distribution of Intelligence Scores. — The distribution of 
intelligence scores is shown in Figure I. The graph, when 
smoothed, will be seen to approach very closely the normal 
curve. So far as intelligence can be used as a criterion, 
this group appears to be a fair sample. The Illinois tests 
were used above the second, while the Holley Picture Com- 
pletion tests were used in the first and second grades. As 
there is no method of reducing the latter to I. Q.'s, all scores 
were reduced to percentages of the median for the class 
instead. The per cent scores were the ones used in plot- 
ting the graph. The distribution of intelligence is shown 
in Figure I. 

The percentages of defects are shown in Table IV. They 
are strikingly near the averages determined from other 
sources. It must be mentioned, however, that these aver- 



28 A Study of the Relation of Some Physical Defects 



65 



60 



55 



50 



45 



40 



35 



30 



25 



20 



15 



10 



LQ 



20 40 60 80 100 120 140 160 180 200 

Distribution of intelligence scores for the grades one to eight, scores first reduced to 
per cent of median of class. 



to Achievement in the Elementary School 29 

ages are from Northern cities ; the data under consideration 
are from a small Southern town. According to the Army 
Draft Board Report, both these items must be taken into 
consideration. For instance, these data show a total per- 
centage of physical defectives of 64 ; while the average for 
New York State (71 per cent), Minneapolis (65 per cent), 
New York City (72 per cent) is a little less than 70 per 
cent. 1 Table IV shows the comparative data. According 
to the Army Report mentioned above, only about 88 per cent 
as many defectives are found in the semirural districts of 
the South as in cities of the North. Taking 88 per cent of 
the 70 per cent would give about 62 per cent, a number very 
near the Humboldt percentage. 

In the same way it has been shown that the 13.4 per cent 
defective vision in Humboldt data approaches very near the 
Northern city average of 18 per cent ; 4.3 defective hearing, 
near the 5.5 per cent average; 27 per cent defective hearing, 
near Ayres' average of 40 to 14 per cent for extreme ages 
of five to fourteen. The comparison is similar for nose, 
tonsils, and teeth, as shown in Table IV. 

TABLE IV 

Showing the Percentages of Defectives in the Humboldt Schools 
Compared With Certain Other Reports- 

Rcports Total Eyes Ears Nose Tonsils Teeth 

Humboldt 64 13.4 4.3 8 27 41.7 

Other sources 703 18-t 5.55 3_236 14-40- 31-65^ 

Method of Attributes. — Some students fall into the habit 
of thinking of statistics as dealing solely with variables and 
overlook entirely the treatment of attributes. To so re- 
strict the meaning of statistics would leave out of consid- 
eration a very large and important class of material. This 
kind of data involves only the counting of those that possess 
and those that do not possess certain characteristics. The 
whole of any selected field of investigation, which is known 
as "the universe," is divided into two groups, called 
"classes." For instance, all men may be classed as "tall" 
or "short." In this study all children are classed as "non- 
defectives" and "defectives." The treatment of this kind 
of data required a different method from that used in the 

^Medical inspection of Schools, Gulick and Ayres. 
J The data are taken from Ayres' Laggards in Our Schools. 

Average of finding in New York State, New York City, and Minneapolis. From 
Medical Inspection of Schools, pages 83-87, by Gulick and Ayres. 
4 Median of finding in fourteen cities. See - above. 
"Ibid, Gulick and Ayres, pages 83-87. 
"Taken from Laggards in Our Schools, page 121. 
"Ibid. See also Chapter 1 of this study. 
s Ibid. See also Chapter 1 of this study. 



30 A Study of the Relation of Some Physical Defects 

study of variables ; but, on the whole, the method is not 
more difficult. The usual procedure is to find what per cent 
of the individuals in the universe is found in one of the 
classes. 

Sometimes it is desirable to make a study of more than 
one attribute of the same object or person. For instance, 
it might be a classification of garden peas into tall and 
dwarfed vines and smooth and wrinkled pods. Some peas 
that grow on tall vines are smooth and some are wrinkled, 
while both smooth and wrinkled may be found on dwarfed 
vines. It is evident that here there would be the four types, 
or "classes" — tall smooth, tall wrinkled, dwarfed smooth, 
and dwarfed wrinkled. This is a fourfold classification. 
This is the way the classes used in this study are deter- 
mined. The positive and negative attributes are high 
achievement or low achievement, and physically sound or 
physically defective. It can be seen that all children fall 
into one of four groups — sound with high scores, sound with 
low scores, defective with high scores, and defective with 
low scores. In this study high and low scores are arbi- 
trarily taken to mean above 100 per cent average achieve- 
ment score and below 100 per cent average score. 

It is often desirable to know what the relation of one 
attribute is to another. It may be that if peas grow on tall 
vines they are more apt to be wrinkled than smooth. 
Where there exists such a cause-and-effect relation, it is 
known as association. If peas growing on tall vines are as 
apt to be wrinkled as smooth, then there is no association 
between tallness of vine and smoothness of peas. This 
study is an attempt to find if such an association exists be- 
tween defects and ability to make high scores on tests in 
school subjects. 

The methods to be used in determining this lead to the 
consideration of Karl Pearson's association formulae. Be- 
fore taking up these formulae, however, methods of classi- 
fying the data will be further considered. 

Grouping the Data. — For use in the criteria of associa- 
tion and in finding the coefficient of correlation, the data 
must be distributed as shown in the diagram below. Start- 
ing with the upper right-hand quadrant and going counter 
clockwise, the first quadrant represents the group of stu- 
dents that had no defects and were making low scores (less 
than 100) at the same time; quadrant II (the upper left- 
hand quadrant), the group that had no defects and were 
making high scores (100 or above) ; quadrant III, those 
making low grades. Pupil 1, Table I, has a median score 
of 78 and has defective vision, so he was checked in quad- 



to Achievement in the Elementary School 



31 



rant IV; pupil 3, with a median of 115 and defective 
tonsils and teeth, was checked in quadrant III. If he had 
not been defective, he would have been checked in quadrant 
II. The attribute "without defects" is designated in this 
study as "A ;" with defects, "a ;" with high scores, "B ;" 
with low scores, "b." Pupil 1 above is represented by "ab," 
while pupil 3 is "aB." A pupil in the first quadrant is rep- 
resented by "Ab ;" one in the second quadrant is indicated 
by "AB." 

Diagram Showing Distribution of Pupils into Four Groups — 
Sound with Low Grades, Sound with High Grades, Defec- 
tive with High Grades, Defective with Low Grades 



Second Quadrant "AB" 
>)»>> >>»>» >>>»> >>>>> 

> > J T > >)!>» >>>>> >!>>> 

" " ' " ' " " etc. 


First Quadrant "ab" 
**>>> nn I ? 7 7 7 7 * t > f > nm »>>>> 
>>>>> >»>»» ?>»»» )>?»» )»>>» >>»»» 


Third Quadrant "aB" 
>>>>> >?>>> >>»>» >»>>» 

9 7 7 7 7 JJJJJ ) ? J > J ! IMI 
,,,,, ,,,,, et( . 


Fourth ( uadrant "ab" 

»>»J> >J»>J ? f } 1 f t > 7 9 f )»>>> >>>J» 
)»>>> )!>>> >>>>> )»)»> >>>?> >»>»> 

" ' " " ' " " ' " ""> etc. 



TABLE V 

Total Defective Eyes, Ears, Nose, Teeth, and Tonsils. Fourfold 
Distribution of Frequencies 



Not Defective 
Above 100% 
AB 

91 


Not Defective 
Below 100% 
Ab 

117 


Defective 

Above 100% 
aB 

97 


Defective 
Below 100% 
ab 

191 



The data for Table V were taken from the distribution 
made in the diagram above. The total defectives below 
100 per cent in score were found to be 191 ; those defective 
and above, 97. The sound or "not defective" below, total 
117; the sound above 100 per cent, total 91. The total 
number of frequencies in this distribution is known as the 
"Universe" and is designated as "N." In this case "N" = 
496. This is the base used in finding the percentages rep- 
resenting the different quadrants. 



32 A Study of the Relation of Some Physical Defects 

Per cent of pupils not defective making below 100% (quad. I) '=.562 

Per cent of pupils not defective making above 100% (quad. II) =.436 

Per cent of pupils defective and making above 100% (quad. Ill) =.336 

Per cent of pupils defective and making below 100% (quad. IV) =.620 

Quadrants I and II represent the sound pupils % of Universe =.419 

Quadrants III and IV represent the defective pupils % of Universe =.581 

Quadrants II and III represent High Scores % of Universe =.379 

Quadrants I and IV represent Low Scores % of Universe =.621 

Association. — Suppose, now, we wish to check the data 
shown in Table V to ascertain if there is an association be- 
tween defects and achievement score. This is easily done 
by reducing each second-order frequency to percentage of 
the Universe and comparing the percentages, or by com- 
paring these second-order frequencies with the correspond- 
ing first-order frequency. By a first-order frequency is 
meant the number of individuals possessing a single attri- 
bute, as Soundness (A) or Defectiveness (a). By a second- 
order frequency is meant the number of individuals pos- 
sessing simultaneously two attributes, as sound bodies and 
high scores (AB), or sound bodies and low scores (Ab). 
They are represented by two letters. These percentages 
would be difficult to interpret without the aid of some kind 
of measure of association, or else have certain criteria for 
judging. Karl Pearson has devised formulae adapted to 
both of these methods. 

Testing the Data by Association Formulae. — If there is 
an association between defective bodies and low scores, the 
following inequalities must hold : 

A? - A_ . AB B AB^Ab. AB.aB 

B " N ' A > N ' B b ' A " a 

The first of these says that the per cent of sound pupils 
among those making a high score should be greater than 
the per cent of sound pupils in the Universe. In simple 
language, the number of sound children with high scores di- 
vided by the total number of children with high scores should 
be greater than the number of sound children in the school 
divided by the number of pupils in school, if there is a posi- 
tive association. The second formula requires that the 
number of sound pupils with high scores divided by the 
number of sound pupils be greater than the number of pu- 
pils with high scores examined divided by the number ex- 
amined, if there is to be a positive association. The third 
requires that the number of sound pupils with high scores 
divided by the number of pupils with high scores' in the 
school be greater than the sound pupils with low scores 
divided by the total number with low scores for positive 
association. The fourth requires that the sound pupils 



to Achievement in the Elementary School 33 

with high scores divided by the number of sound pupils in 
the Universe be greater than the defective pupils with high 
scores divided by the defective pupils examined. Any one 
of these would indicate an association, but the application 
of the four is further proof of it. 

If the data from Table V be used to illustrate the method 
described above, then A = 208 (sound) ; B (with high 
scores) = 188; a (defective) =388; b (low scores) = 308; 
N (Universe) =496; AB (sound with high scores) =91; 
Ab (sound with low scores) = 117; ab (defective with low 
scores) = 191. These numbers substituted in the formulae 
give: 

91' 208 .„, , in 91 188 ,„„ n „ n 

188 > 496' -484 .419; ^ ^ ; .436 .379 

91 117 AOA or7ft 91 97 

188 > 308 : - 484 - 379 = 208 > 288' -436 >. 336 

The inequalities all prove true. This means, then, that 
the per cent of bright pupils in the sound group is greater 
than the per cent of pupils with high scores in the whole 
group ; that the per cent of sound pupils among those with 
high scores is greater than the per cent of sound pupils 
among the whole group ; that the per cent of sound among 
those with high scores is greater than the per cent of sound 
among the pupils with low scores ; and that the per cent of 
those with high scores among the sound is greater than 
the per cent of high scores among the defectives. Since 
these all agree and the left-hand member in each inequality 
is greater than the right, the conditions between defects 
and low scores are all met. Therefore it must be concluded 
that there is a positive association between these two traits. 

Testing the Degree of Association. — If the inequalities 
were noticeably large when determined as above, the degree 
of association would probably be large; but when the per- 
centages are nearly equal, it is difficult to estimate the de- 
gree of association. To aid in the interpretation of the 
results, another formula is used. If A, B, a, and b have 
the same meaning as above and if the coefficient of correla- 
tion is indicated by Q, the formula below will give the degree 
of association. This formula is such that as the association 
increases, the value of Q increases from to +1 ; and as the 
disassociation, or negative association, increases, Q de- 
creases from to — 1. 



34 A Study of the Relation of Some Physical Defects 
(AB) (ab) — (Ab) (a B) 



Q = 



(AB) (ab) + (Ab) ■ (a B) 



When the data from Table V is substituted, the equation 
becomes : 



Q 



(91) (191) — (117) (97) 
(91) (191) + (117) (97) 

17381 _ 11344 5937 



17381 + 11344 ~ 18725 



21 



This result shows positive association, because the prod- 
uct of the sound with high scores and the defective with 
low scores is greater than the product of the sound with 
low scores and the defective with high scores. This is the 
same as saying that if the product of the second and fourth 
quadrants is greater than that of the first and third, the 
association is a positive one. A glance at Table V will make 
this fact clear. As the product of the first and third quad- 
rants approaches zero, the value of Q approaches 1, since 
the numerator and denominator of the fractions are then 
equal, each being the product of the second and fourth quad- 
rants. As the product of the second and fourth quadrants 
approaches zero, Q approaches — 1, since the numerator and 
denominator are then equal, each being the product of the 
first and third quadrants. This coefficient, then, is the 
ratio of this excess or deficit to the sum of the products of 
the two pairs of opposite quadrants. 

This coefficient of .21 indicates that if a single child were 
selected at random from this school, the chances favor its 
being one with high scores, if it be one without physical de- 
fects. This is especially true, since the probable error of 
this coefficient is small, as will be seen from the application 
of the probable error formula : 

iP. E. = .67449x1 — r 2 



/N 

Here r — .21 and N = 496. Putting these values in the 
formula, 

i or-' Q^Q 

P.E. = .67449 J^ - .67449 ^jgL : ± .«, 

Then r = .21 ± .03 



^ugg, Statistical Method Applied to Education, page 273. 



to Achievement in the Elementary School 35 

This interpreted means that the coefficient of association 
lies between .18 and .24 in half of the cases, or with a prob- 
ability of 1 : 1. 

While the probable errors shown in Table VII, Chapter 
IV, were derived by the above formula, they should be con- 
sidered only as near approximations. In a strictly math- 
ematical sense, probable error formulas that apply to vari- 
ables do not apply to attributes. 1 An absolute correction 
can be obtained by using Pearson's Formula- for a fourfold 
table as follows: 



P.E. 



.67449 

/N A - r J / 1 — ( sin"" 1 r)- 

( 90 )-' 



h ( 1 -a ) h( 1 + a) / |il -a ) ( 1 -a) 
H K 

Here N and r have the same meaning as in the formula 
on page 34; sin ' can be found by finding an angle whose 
sine is "r" ; J (1 — a), \ (la), \ (l_ a ,), and \ (l + a 2 ) 
are percentages representing the relative areas included 
under the normal curve as shown by Sheppard's tables (see 
footnote, page 37). H and K are the values of Z for col- 
umns and rows, respectively, and can be read from Shep- 
pard's tables. 

The data from Table V substituted in this formula give : 



■67449 /i .21-' 1 12i J /.621 .379 



.419 x .581 
.38022 



(90)-' .39104 

P. E. = .043 



This shows an increase over the probable error found 
above of .01. 

If access is had to Sheppard's Tables, Miss Gibson's Ta- 

67449 
bles :! for 1 , and Everitt's Tables of Tetrachoric Func- 

/N 
tions, 4 this formula should be used for fourfold tables in- 
stead of the ordinary formula. Without Sheppard's tables, 

^ule, Introduction to the Theory of Statistics, page 352. 

-Blometrika, Vol. IX, page 22. 

3 Biometrika, Vol. IX, page 25. 

<Biometrika, Vol. VII, page 436, and Vol. VII, page 385. 



36 A Study of the Relation of Some Physical Defects 

it cannot be used; and, with them, the amount of work 
required is extreme unless Gibson's and Everitt's tables are 
also accessible. 

A Method of Correlation that is Adapted to a Variable 
and an Attribute. — The method used above does not take 
advantage of the fact that one of the attributes was a meas- 
urable quantity. The scores yield themselves most readily 
to this kind of treatment. Pearson 1 has given us a formula 
for utilizing this property and at the same time making it 
possible to correlate with a nonmeasurable attribute. 2 

At first sight the formula seems complex, because it is 
derived from the equation of the normal curve and con- 
tains integral signs. It is as follows : 

ly 2 



N /~00 2 o--r 

W^f J y ye ' dy 



N /»oo y 

2 n a-> J y e 2 *? dy 



(1) 



r^=- - i (y>--0- 
'2n . e 2 Ky/ 



1 ,oo 1 ., I (1 — a) 

'2lf J y/0-2 e 2 y dy 



(2) 



But p = r en ± .'. p == r <n* j ( i - a) 



, p Z o-i HI — a) p (£ , 
andr=— ! =- -— — 7 = — ^ — = — —, (4) 



0"! 



(1 — a) _Z o-i Z 

(1-a) 



In these equations p and q are the coordinates from a 
point on the regression line, r the coefficient of correlation ; 
o-i and o-i are the standard deviations for the two variables ; 
e-^y 2 is the logarithmic function that gives the normal 

J Karl Pearson A New Method of Determining Correlation Between a Measured 
Character A and' a Character B, of which Only the Percentage of Cases Wherein B 
Exceeds a Given Intensity is Recorded for Each Grade of A.—Biometrika, Vol. Vll, 
page 98. 

-See note, page 46. 



to Achievement in the Elementary School 



37 



curve ; Z is an abbreviation for the numerator of the right- 
hand side of equation 2 above; .] (1 — a) is the denomina- 
tor of the same fraction. Sheppard has worked out the 
values of the last two expressions — Z and -\ (1 — a) — and 
has made a table to be used in finding the area under the 
normal curve. p can be found by subtracting the mean 
of the whole distribution from the mean of one array. The 
standard deviations of the whole distribution and that of 
the single array can be found. Z and \ (1 — a) can be 
taken from Sheppard's tables. 1 Thus everything needed in 
the solution of equation 4 above is easily obtainable. 

The application of this formula to a specific set of data 
will help to clear it up. It is desired to find the correlation 
betv/een defective tonsils and scores in spelling. The data 
in the table on the following page were used to represent 
the method. The first column is the scores ; the second, the 
frequencies for the group without defects ; the third, the 
frequencies for the group with defects ; the fourth, the to- 
tals, d, fd, fd-, columns were used in finding the standard 
deviation of the whole distribution ; the last two columns 
were used for finding the mean of the array of defectives. 
These, with the values of Z and \ (1 — a) from the tables, 
enable us to solve for r. 



TABLE VI 

Correlation Between Scores in Spelling and Defective Tonsils 



Per Cent Sound Defective Total 



fd 



id? 



d 



df 



10 


7 


2 


9 


—8 


—73 


576 


—8 


—16 


20 


6 


2 


8 


—7 


—56 


392 


—7 


—14 


30 


7 


2 


9 


—6 


—54 


324 


—6 


—12 


40 


8 


6 


14 


—5 


—70 


350 


—5 


—30 


50 


20 


5 


23 


—4 


—92 


368 


—4 


—20 


60 


19 


4 


23 


—3 


—67 


307 


— 3 


—12 


70 


18 


11 


29 


—2 


—56 


116 


—2 


—22 


80 


38 


8 


46 


—1 


—46 


46 


—1 


— 8 


90 


15 


17 


32 

















100 


29 


9 


38 


1 


38 


38 


1 


9 


110 


44 


13 


57 


2 


114 


238 


2 


26 


120 


28 


5 


33 


o 

o 


99 


397 


3 


15 


130 


14 


2 


16 


4 


64 


256 


4 


8 


140 


8 


5 


13 


6 


65 


325 


5 


25 


150 


O 

o 


3 


6 


6 


36 


216 


6 


18 


160 


1 





1 


7 


7 


49 


7 





170 


6 


2 


5 


8 


30 


320 


8 


16 


180 





1 


1 


9 


9 


81 


9 


9 


190 


1 





1 


10 


10 


100 


10 





200 


5 





5 


11 


55 


605 


11 





Totals 


314 


95 


409 




20 


4895 




8 




pard's 


Tables, B 


ometrika. 


Vol. II. page 


182. 








'Shep 





38 A Study of the Relation of Some Physical Defects 

Mean of total distribution, 97.885 ; mean for defectives, 
94.158. Standard deviation for the total distributions, 



.0025 = 3.341 



409 



P 3 797 

Then ^—^ = (94.158 — 97.885) -^ 33.41 



33.41 "" x -■•— , . ~~.^- 3341 

£(1 _ a) = -r£ = .2322 ; then i (1+a) = 1 —.2322 =.7678 
From Sheppard's tables this gives Z — .3056. Then 

3.727 .2322 = .865409 = 
r 33.41 .3655 10.210096 

It will be noted that the result shows a negative correla- 
tion between defects and high scores which would give a 
positive correlation between defects and low scores. 

A table of similar results is shown in the next chapter 
for each defect with specific subjects. 

It will be remembered that it was the aim of this study, 
as set forth in the outset, to get the apparent correlations 
and then to free them from the influence of certain factors 
that might affect these coefficients. This has been done, 
and the following is an extract of the process as applied to 
the correlation between tonsils and spelling. The formula 
used is Pearson's and is taken from Yule's Introduction to 
the Theory of Statistics, page 238. 1 

v _ ^12,34 . . , (n — 1) ' Pin 34 . . . . (n -1) •^2n.34 . . . . (n - 1) 

* 12.34. n— /-, _ 2 W1 _ 2 ; rf~ 

V- 1 - x ln34 . . . .(n — 1)) K*- 1 2n.34. . . .(n—\)) 

The formula for three variables is : 

y ^12 ^13 ' ^23 

123 = " (l-ryMi-r!) 4 

In another place in this report the correlation of sound 
tonsils with Illinois intelligence scores gave a coefficient of 

^t should be remembered here that these partial coefficients of association might 
have been found in a way similar to that for testing for simple associations. Yule 
discusses this method and furnishes criteria for testing for partial association, but the 
method is complex and is less refined than the regular correlation formula used here. 
The latter is far better here, because in each case one of the traits is expressed as a 
variable, and in case of intelligence and scores both are variables. 



to Achievement in the Elementary School 39 

.04 ; of Illinois intelligence and median achievement scores, 
.32 ; tonsils and spelling scores, .10. Substituting these val- 
ues in the formula, we have : 

ru = .04; rss .32; ta .10, 

where the figures 1, 2, 3 stand for the variables and attri- 
butes, tonsils, achievement scores, and intelligence scores, 
respectively. 
These give : 

.10 (.04) (.32) 
ri2 3 (1 .0016) • (1 .1024) » 

.057200 noo 
Tl2 " .943000 ~ ' 0J2 



CHAPTER IV 

PRELIMINARY ANALYSIS, USING PERCENTAGES AND 
ASSOCIATION COEFFICIENTS 

This chapter deals with the tabulated data derived by the 
methods outlined in Chapter III. Tables VII to XII, inclu- 
sive, show the distribution of the data according to the va- 
rious traits. Table XIII is a summary of these. Tables 
XIV to LIII contain the data from which the coefficients of 
association between each defect and the specific subjects 
are derived. These forty coefficients are summarized in 
Table LIV. These are the coefficients as they appear before 
being freed, by the formula for partial correlations, from 
the influence of other factors. 

Defects Correlated with General Ability 

table VII 

All Defects Correlated with General Ability 





Scores Above 100% 


Scores Below 100% 


Totals 


Without Defects 


AB, 91 


Ab, 117 


208 


With Defects 


aB, 97 


ab, 191 


288 


Total 


188 


308 


496 



In Tables VII to XII the following notation should be 
observed : 

N — Total number of observations, the "Universe." 

A — Number of individuals without defects. 

a — Number of individuals with defects. 

B — Number of individuals scoring above 100% of class 
median. 

b — Number of individuals scoring below 100% of class 
median. 

AB — Number of individuals without defects making 
above 100%. 

Ab — Number of individuals without defects making be- 
low 100%. 



to Achievement in the Elementary School 41 

aB — Number of individuals with defects making above 
100%. 

ab — Number of individuals with defects making below 
100%. 

A full explanation of the formulae used in testing the 
association is made in Chapter III, page 43. It is suffi- 
cient here to state that the left-hand members of the fol- 
lowing inequalities must be greater than the right-hand 
members and to repeat enough of the process to visualize 
the results : 



AB A 


AB B AB Ab . AB . 


aB 


B N 


' A N ' B b ' A 


a 


Q 


(AB ab) (Ab aB) 




(AB ab) + (Ab aB) 




These give : 


_91>208 484 :> i419 
108 496 

I>1«'« - 379 





_9K HZ 

108 308 

_9i^ jn 

208 288 



or .484 .379 



or .436 > .336 



Which show there is positive association. If the left- 
hand members were smaller than the right, a negative asso- 
ciation would be indicated. To find the degree of associ- 
ation, as was done on page 34 of this study, the following 
substitution is made in the formula for Q : 

(91 191) — (117x97) 5937 __ n 

M " (91 191) + (117x97) 18725 _ 

In Chapter III the probable error of this coefficient was 
found to be == .03. This indicates a rather significant de- 
gree of association between general ability as shown by 
scores and physical soundness. 1 

'Karl Pearson interprets a coefficient of association of .076 between good tonsils 
and weight as significant.— Iiiometrika. Vol. VII, page 103. 



42 A Study of the Relation of Some Physical Defects 

TABLE VIII 

Tonsils Correlated with General Ability 





Scores Above 100% 


Scores Below 100% 


Totals 


Without Defects 


AB, 144 


AB, 218 


362 


With Defects 


aB, 44 


ab, 88 


132 


Total 


188 


306 


494 



Substituting in the formula above 



144 362 . 

188 ^ 494 • 766 ^ ' 732 



144 ^ 188 
36 ^ 496 

144 ^ 218 
494 > 132 



: .398 > .380 
: .766 > .712 



These inequalities indicate a positive correlation the de- 
gree of which is shown by : 



Q 



(144x88) — (218x44) 
(144x88) + (218x44) 



,138 ± .044 



This coefficient is also large enough to show that sound 
tonsils and general achievement are related significantly. 

TABLE IX 
Eyes (Vision and Eyes) Correlated with General Ability 





Scores Above 100% 


Scores Below 100% 


Totals 


Without Defects 


AB, 170 


Ab, 276 


446 


With Defects 


aB, 18 


ab, 31 


49 


Total 


188 


307 


495 



to Achievement in the Elementary School 



43 



From the formula the data in this table give : 

170 188 

446 ' 505 

170 446 

188 505 



p= : .381 .372 



.904 



Q 



170 


276 


188 


307 


170 


18 


446 


49 


(170 31) 





.904 .899 



.381 .367 



(276 18) 



(170 31) + (276 18) 



,029 



.(»: 



There is but slight indication of a positive association 
between sound eyes and high scores. As will be shown 
later, this coefficient varies with different subjects, some 
showing a negative correlation. As stated in the introduc- 
tion, Ayres and Cornell report negative or slight positive 
correlation between sound eyes and teachers' marks. 

TABLE X 
Correlation of Defective Nasal Cavities with Achievement 





Scores Above 100' , 


Scores Below 100' , 


Totals 


Without Defects 


AB. 185 


Ab, 280 


465 


With Defects 


aB, 2 


ab, 27 


29 


Total 


187 


307 


494 



It follows that 



185 
187 
185 
465 
185 
187 
185 
465 



465 
494 
187 
494 
280 
307 
_2 
29 



.989 .941 



.397 .378 



.987 .912 



.397 > .069 



_ (185x27) -(280 x2) 
H ~ (185x27) - (280x2) '' yy ~ >UiD 



44 A Study of the Relation of Some Physical Defects 

This is is by far the most significant coefficient found. 
There is evidently a high degree of association between 
mouth breathing or nasal obstruction and backwardness in 
subjects. This conclusion is also supported by Ayres in 
his study of promotions in his Laggards in Our Schools. 
It will be noticed that all pupils, except two, with nasal 
obstructions made less than 100% as an average achieve- 
ment score. 

TABLE XI 

Correlation of Soundness of Teeth with Achievement Scores 





Scores Above 100% 


Scores Below 100% 


Totals 


Without Defects 


AB, 134 


Ab, 184 


318 


With Defects 


aB, 53 


ab, 136 


189 


Total 


187 


320 


507 



134 318 . 

187 507 • 



.627 



134 . 184 . 

187 '' 320 * 



.593 



134 
318 



187 
507 



.421 



.362 



134 

318 



_53 

189 



.421 



.280 



Q = 



(134x136) — (184x53) 
(134x136) + (184x53) 



.302 ± .02 



The degree of positive association of sound teeth with 
achievement is larger than might have been expected. This 
is probably due in part to the fact that a large number of 
those having defective teeth also have other defects. 



to Achievement in the Elementary School 45 

TABLE XII 
Correlation of Hearing with High Scores 





Scores Above 100% 


Scores Below 100' < 


Totals 


Without Defects 


AB, 180 


Ab, 284 


464 


With Defects 


aB, 7 


ab, 23 


30 


Total 


187 


307 


494 



These data indicate positive association. The inequali- 
ties are: 

180 464 . 

187 494 • ,aW •* W 

1 1 : - 903 > - 398 

1 i ■■ - 9037 - 398 

ISO 7 

ii -35 : - 903 - 233 

_ (180x23) -(284x7) 
y " (180x23) + (284 x 7) "^ - UaJ 

Next to obstructed breathing, this is the largest coeffi- 
cient of association found between defects and general 
achievement. There is probably some relation between ob- 
structed breathing and defective hearing; but to what 
extent, this study does not undertake to determine. 

TABLE XIII 

Summary of Data Showing Relation of Specific Defects to 
Achievement Scores 

Defects Ab AB aB ab Q P.E. 

Hearing 284 180 7 23 .351 .059 

Tonsils 218 144 44 88 .138 .044 

Nasal Obstruction 280 185 2 27 .799 .016 

Eyes and Vision 276 170 18 31 .029 .0.44 

Teeth - 184 134 33 136 .302 .02 

General Defects 117 91 97 191 .21 .03 



46 A Study of the Relation of Some Physical Defects 

Table XIII, Summary. — If the probable effect of other 
factors is ignored, it is evident that there is indication of a 
positive association between each of the defects mentioned 
in Table XIII and general ability. Nasal obstruction, which 
usually results in mouth breathing and is often accompa- 
nied by defective hearing, appears to be a greater handicap 
than either of the others tabulated. The high coefficient of 
.799, with a probable error of : .016, would justify the 
statement that should an individual with defective tonsils 
be selected from the Humboldt School, he would very prob- 
ably be one that would be low on tests. The same could be 
said of hearing, except that the probability would be less, 
though the coefficient .351 ± .059 is not a low correlation. 
That for teeth with Q = .302 ± .04 shows the next highest 
indication of a positive relation. Defective tonsils show a 
negligible correlation with scores, .138 ± .044. This, at 
the most, can only be taken as a slight indication of positive 
association. Defective eyes and vision give almost a zero 
correlation, .029 ± .044. In fact, it will be shown later 
that with some subjects this coefficient becomes negative. 

Relation of Defects to Special Abilities 

The discussion immediately above was based upon the 
average ability of the child as represented by the median of 
his per cent scores. In order to see if certain defects are 
a greater handicap than others in relation to special sub- 
jects, or if a particular defect affects progress in one sub- 
ject more than in another, the subjects will be dealt with 
separately. In this process the frequencies are smaller and 
the range is often as great as for the whole distribution. 
For this reason a formula that utilizes the influence of this 
wide range is substituted for the fourfold association for- 
mula. It is based on a decile distribution. As a full and 
complete discussion of this formula may be found on page 
36, Chapter III, the discussion will be omitted here. 1 

TABLE XIV 

Correlation of Hearing with Trabue Completion Scores 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 


Total 


S 
D 


3 4 4 9 9 32 19 47 106 40 36 19 13 3 4 2 
. 11222 1 2 2 1 1 . 


1 


2 


353 
15 












T 


3 __ 4 4 10 10 34 21 49 107 42 33 20 14 3 4 2 


1 


2 


368 



S, nondefective ; D, defective; T, total distribution. 



1 The coefficients of mean square contingency deduced from such tables will be 
comparable among themselves, but possibly 30 to 50 per cent below the true value of 
the correlation coefficient. Tables worked out by the fourfold table method show, on 
am average, 40 per cent increase on the contingency values. It is only needful to 
bear this in mind when considering the absolute importance of the contingencies in- 
vestigated. — Biometrika, Vol. VII, page 223. 



to Achievement in the Elementary School 47 

Mean of total distribution, 88.33; mean of defectives, 
93.66. 

Standard deviation of total distribution, 27.20. 

£ (1 — a) = .0402, \ (1 + a) = .9598, Z = .0863 

5.33 .0402 



27.20 .0863 



.092 



Thus children are somewhat more likely to make high 
scores on the Trabue Completion Test if they do not have 
defective hearing. 

TABLE XV 

Correlation of Eyes and Vision with Trabue Completion Scores 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 Total 


S 
D 


3 —348 8 33 17 44 100 40 32 19 11 3 3 2 
1 _.. 2 2 1 4 5 7 2 E 1 3 1 


1 


1 332 
1 36 


T 


3 __ 4 4 10 10 34 21 49 107 42 38 20 14 3 4 2 


1 


2 368 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 93.665 ; mean of defectives, 
95.833. 

Standard deviation of total distribution, 27.20. 

-J (1 + a) =.9020, HI — a) =.0980, Z = .1725 

2.168 .0980 



27.20 .1725 



.045 



This coefficient indicates that there is a negative asso- 
ciation between sound eyes and ability, as measured by the 
Trabue Tests. This probably means that the more studious 
develop defective eyesight. 

TABLE XVI 

Correlation of Nasal Obstruction with Trabue Completion Test 





Achievement Scores Expressed as Per Cent of 


Median 








10 20 30 40 50 60 70 80 90 100 110 120 130 140 


150 


160 


170 


180 Total 


s 

D 


3 _ 4 4 X 10 32 19 44 98 41 36 19 13 3 
2 __ 2 2 5 9 1 2 1 1 __ 


3 
1 


2 


1 


2 342 

2(i 


T 


3 _. 4 4 10 10 34 21 49 107 42 38 20 14 3 


4 


2 


1 


2 368 



S, nondefective; D, defective; T, total distribution. 



'In keeping with Pearson's practice, r is used to represent the coefficient of asso- 
ciation when derived by the above formula. As indicated in note, page 46, these 
r's must be increased about 40% to make them comparable with the Q's. 



48 A Study of the Relation of Some Physical Defects 

Mean of total distribution, 93.665 ; mean of defectives, 
92.308. 

Standard deviation of total distribution, 27.20. 

i (1 _ a ) = .0708, HI + a) =.9292, Z = .1354 
1.357 .0708 



27.2 .1354 



.026 



While this coefficient is small, it is large enough to indi- 
cate that there is a positive association between nasal ob- 
struction and ability as shown by the Trabue Tests. 

TABLE XVII 

Correlation of Teeth with Trabue Completion Test 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 Total 


S 
D 


3 2 3 9 8 23 8 25 68 25 20 15 10 2 4 1 
2 1 1 2 11 13 24 39 17 18 5 4 1- __ 1 


1 


2 318 
50 


T 


3 _. 4 4 10 10 34 21 49 107 42 38 20 14 3 4 2 


1 


2 368 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 93.665 ; mean of defectives, 
92.5. 

Standard deviation of total distribution, 27.20. 

i (1 — a) =.1866, $ (1 + a) = .8134, Z = .2684 

1,165 ,1866 
27.20 .2684 ' 

Thus defective teeth and low scores are slightly, but 
probably significantly, associated. 



TABLE XVIII 

Correlation of Sound Tonsils with Trabue Completion Test 

Scores 



Achievement Scores Expressed as Per Cent of Median 







10 20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 200 Total 


s 

D 


2 
1 


. 2 
__ 2 


4 7 9 22 15 35 82 30 27 15 8 2 3 2 __ 2 
3 1 12 6 14 25 12 11 5 6 1 1 1 


261 
101 


T 


3 


. 4 


4 10 10 34 21 49 107 42 38 20 14 3 4 2 1 2 


362 



S, nondefective; D, defective; T, total distribution. 



to Achievement in the Elementary School 49 

Mean of total distribution, 93.665 ; mean of defectives, 
93.81. 

Standard deviation of total distribution, 27.20. 

i (1 — a) =.2790, HI + a) =.7210, Z = .1988 

.145 .2790 



27.20 .1988 



= .0062 



There is a positive association between sound tonsils 
and high scores on the Completion Tests, but it is so slight 
as to make it negligible. 

TABLE XIX 

Correlation of Nasal Obstruction with Low Scores in Reading 



Achievement Scores Expressed as Per Cent of Median 




10 


20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


1 


3 4 12 15 21 31 20 29 41 43 29 15 S 15 6 1 1 
-246135_1 1. 


5 


3 330 
24 










T 


1 


3 4 12 17 25 37 21 32 46 43 30 15 1 16 6 1 1 


5 


3 359 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 100.363 ; mean of defectives, 
83.75. 

Standard deviation of total distribution, 36. 

i (i _ a) = .0727, 4 (1 + a) = .9273, Z = .1374 

16.613 .0727 



36 .1374 



= .244 



This coefficient of association between nasal obstructions 
and low scores deserves special mention, as it is the most 
significant of any found between defects and ability in spe- 
cial subjects. A child's ability to read rapidly seems to be 
closely associated with his soundness as to nasal breathing. 

TABLE XX 

Correlation of Tonsils with Reading Rate Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


3 
2 


3 


4 9 13 11 28 18 22 34 29 31 11 5 12 5 1 1 
__ 3 4 14 9 3 10 12 14 9 4 3 4 1 __ __ 


4 

1 


3 237 
93 


T 


5 


:; 


4 12 17 25 37 21 32 46 43 40 15 8 16 6 1 1 


5 


3 330 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 100.363 ; mean of defectives, 
98.118. 

Standard deviation of total distribution, 36.04. 



50 A Study of the Relation of Some Physical Defects 
i (1 — a) =.2818, i (1 + a) =.7182, Z = .3362 

2.245 .2818 



36.04 .3362 



.044 



This coefficient indicates that there is at least some asso- 
ciation between defective tonsils and reading rate. 

TABLE XXI 
Correlation of Defective Teeth with Reading Rate Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


3 
2 


1 
2 


1 7 9 9 20 11 20 23 32 14 11 5 9 3 1 1 
3 5 8 16 17 10 12 23 11 16 4 3 7 3 __ __ 


4 
1 


2 186 
1 144 


T 


5 


3 


4 12 17 25 37 21 32 46 43 30 15 8 16 6 1 1 


5 


3 330 



S, nondef ective ; D, defective; T, total distribution. 
Mean of total distribution, 100.563 ; mean of defectives, 
95.7638. 

Standard deviation of total distribution, 36.04. 

i (1 — a) =.4363, | (1 + a) =.5637, Z = .3935 

_ 4.7992 .4363 _„ 

" 36.04 .3935 ' 

There is quite a sensible correlation between defective 
teeth and low scores, much of which is probably due to in- 
fluence of bad teeth on general health. 

TABLE XXII 

Correlation of Hearing with Reading Rate Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


5 




3 



4 12 15 23 25 19 31 42 41 28 15 8 16 6 1 1 
0022221422000000 


5 



3 313 
17 


T 


5 


3 


4 12 17 25 27 21 32 46 43 30 15 8 16 6 1 1 


5 


3 330 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 100.563; mean of defectives, 
98.118. 

Standard deviation of total distribution, 36.04. 



to Achievement in the Elementary School 51 

I (1— a) == .05151, \ (1 + a) = .94849, Z = .10567 

9.0920 .05151 12 „ 
36.04 .10567 

This coefficient is large enough to indicate quite a positive 
association of hearing with rate of reading. 

TABLE XXIII 
Correlation of Eyes with Reading Rate Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 1G0 170 180 


190 


200 Total 


S 
L> 


5 




3 



3 12 15 23 33 17 26 42 37 27 11 8 16 5 1 1 
1022446463400100 


4 

1 


2 291 
1 39 


T 


5 


3 


4 12 17 25 37 21 32 46 43 30 15 8 16 6 1 1 


5 


3 330 



S, nondefective ; D, defective; T, total distribution. 
Mean of total distribution, 100.060 ; mean of defectives, 
104.717. 

Standard deviation of total distribution, 36.09. 

J (1 — a) =.1121, i(l + a) =.8879, Z = .19070 

_ 4.657 .1121 _ 75g 

r " ~36^9~ 719070 — 0758 

As might have been expected from what is known of the 
relation of defective eyes to other subjects, as shown in the 
above tables, good vision shows a negative association with 
scores. 

TABLE XXIV 
Correlation of Hearing with Reading Comprehension Scores 



Achievement Scores Expressed as Per Cent op Median 







10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 


ISO 


L90 


200 Total 


s 
l) 


2 



8 



a 
i 


8 15 17 25 40 23 28 35 14 22 13 8 14 10 5 
110130033211001 


3 



5 



5 306 
18 


T 


•J 


8 


9 


9 16 17 26 43 23 28 38 17 24 14 9 14 10 6 


3 


5 


5 324 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 96.697; mean of defectives, 
97.777. 

Standard deviation of total distribution, 42.5. 



52 A Study of the Relation of Some Physical Defects 



i (1 — a) = .0555, HI + a) =.9445, Z = .1127 
1.080 .0555 ni1 

r= ~m~ ^127 =- 011 

The indications are that comprehension in reading is not 
associated to any appreciable extent with defective hearing. 
What association there is, is probably negative. 

TABLE XXV 

Correlation of Teeth with Reading Comprehension Scores 



Achievement Scores Expressed as Per Cent of Median 







10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


s 

D 


2 




6 
2 


3 
6 


4 8 4 15 24 12 14 21 7 15 10 6 6 5 4 2 

5 6 13 11 14 11 14 17 10 9 4 3 8 5 2 1 


4 
1 


5 177 
147 


T 


-1 


8 


9 


9 14 17 26 38 23 28 38 17 24 14 9 14 10 6 3 


5 


5 324 



S, nondef ective ; D, defective; T, total distribution. 
Mean of total distribution, 96.697; mean of defectives, 
92.347. 

Standard deviation of total distribution, 42.5. 

£ (1 — a) =.4851, 1(1 + a) =.6149, Z = .10567 

4.35 .4851 



42. 5 . 3896 



.124 



The association of sound teeth with high reading com- 
prehension scores is large enough to be significant. 

TABLE XXVI 

Correlation of Freedom from Nasal Obstructions with Reading 
Comprehension Scores 



Achievement Scores Expressed as Per Cent op Median 







10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


s 
1) 


•1 


8 


8 
1 


7 12 15 23 40 20 25 35 16 24 13 9 13 10 6 3 
222333331 1 1 


5 


5 299 
25 










T 


■1 


8 


SI 


9 14 17 26 43 23 28 38 17 24 14 9 14 10 6 3 


5 


5 324 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 96.697; mean of defectives, 
93.4. 

Standard deviation of the total distribution, 42.50. 



to Achievement in the Elementary School 53 

I (1 — a) =.07716, HI + a) =.92284, Z = .14453 
3.297 .07716 



36.04 .14453 



.042 



This coefficient indicates that there is at least a slight 
negative association between nasal breathing and compre- 
hension scores in reading. 



TABLE XXVII 

Correlation of Sound Tonsils with Reading Comprehension 

Scores 



Achievement Scores Expressed as Per Cent of Median 







10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


!90 


200 Total 


s 
I) 


2 


7 
1 


8 
1 


8 9 13 19 33 13 20 24 10 17 6 4 12 7 5 3 
1 5 4 7 10 10 8 14 7 7 8 5 2 3 1 ._ 


5 


3 22S 
2 96 


T 


■1 


8 


9 


9 14 17 26 43 2:5 28 38 17 24 14 9 14 10 6 3 


5 


5 324 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 96.697 ; mean of defectives, 
100.833. 

Standard deviation of the total distribution, 42.50. 

I (1 — a) = .2960, HI + a) =.7040, Z = .3457 

r = " 4 - 14 - 2960 - = _071 

42.50 .3457 

This coefficient shows a slight negative association be- 
tween sound tonsils and reading comprehension scores. 

TABLE XXVIII 
Correlation of Eyes and Vision with Reading Comprehension 



Achievement Scores Expressed as Per Cent of Median 







10 


■jo 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 

n 


■1 


8 


1 


9 14 14 24 35 21 23 31 15 21 12 9 13 10 6 3 
3 28257232 1 


5 


4 287 
1 37 










T 


■1 


8 


9 


9 14 17 26 43 23 28 38 17 24 14 9 14 10 6 3 


5 


5 324 



S, nondefective; D, defective; T, total distribution. 
Mean of total distribution, 96.097 ; mean of defectives, 
95.54. 

Standard deviation of total distribution, 42.91. 



54 A Study of the ReloMon of Some Physical Defects 
i(l_ a) =.1142, £ (1 + a) =.8858, Z = .19302 

r= __557_ ^142_ = .o076 
42.91 .19302 

The association between good eyes and vision and reading 
comprehension, while positive, is negligible. 

TABLE XXIX 

Correlation of Hearing with Geography Scores 

Achievement Scores Expressed as Per Cent of Median 
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 

S 2 _ 8 6 6 16 26 35 46 37 20 18 9 4 3 7 3 246 

D 1—1 3 3 3 2 4 3 2 __________ — — — 22 

T 3~T. 1 8 6 6 19 29 38 48 41 23 20 9 4 3 7 3 268 

S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 95.222; mean of defectives, 
86.819. 

Standard deviation of total distribution, 30.67. 

i (1 — a) =.0820, -I (1 + a) =.9180, Z = .1508 

8.403 .0820 14g 

" 30.67 .1508 ' 

It is evident from this correlation that progress in the 
Humboldt schools in geography is rather highly associated 
with acuteness of hearing. It will be observed from the 
summary at the close of the chapter that defective hearing 
is more highly associated with geography than with any 
other subject in the curriculum. 

TABLE XXX 

* Correlation of Eyes and Vision with Geography Scores 

Achievement Scores Expressed as Per Cent of Median 

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 

S 2 __. 1 7 6 4 17 26 33 42 37 19 19 8 4 3 6 • - 3 238 

D 1 1 __. 2 2 3 5 6 4 4 __ 1 __ __ 1 ______ __ 30 

T 3 __. 1 8 6 6 19 29 38 48 41 23 19 9 4 3 7 . 3 268 

S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 95.52 ; mean of defectives, 
89.33. 

Standard deviation of total distribution, 30.67. 



to Achievement in the Elementary School 55 

HI — a) =.1119, |(1 + a) =.8881, Z = .1977 
6.2167 .1119 



30.67 .1977 



.114 



Contrary to what has been observed between soundness of 
vision and other subjects, this coefficient indicates a rather 
high association between vision and geography scores. 

TABLE XXXI 
Correlation of Nasal Obstruction and Low Scores in Geography 

Achievement Scores Expressed as Per Cent of Median 
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 

S 3 _.. 1 7 6 6 15 24 35 42 39 18 20 9 4 3 7 3 242 

D 1 4 5 3 6 2 5 __ __ __ __ __ __ __ __ __ 26 

T 3 _.. 1 8 6 6 19 29 38 48 41 23 20 9 4 3 7 . 3 268 

S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 95.222 ; mean of defectives, 
87.693. 

Standard deviation of total distribution, 30.67. 

|(1 — a) =.097, 1(1 a) =.903, Z = .17136 

7.529 .097 

r " 30.67 .17136 

This coefficient indicates a rather high degree of associ- 
ation between nasal obstructions and low scores in geogra- 
phy. 

TABLE XXXII 
Correlation of Teeth with Geography Scores 



Achievement Scores Expressed as Per Cent of Median 







10 20 


30 40 50 60 70 «0 90 100 110 120 130 140 150 160 170 180 190 


2"" Total 


S 


3 


1 


3 3 3 9 13 17 25 15 15 14 3 3 3 5 . 

5 3 3 10 16 21 23 26 8 6 6 1 2 


2 137 
1 131 










T 


3 


1 


8 6 6 19 29 38 48 41 23 20 9 4 3 7 


3 268 



S, nondefective; D, defective; T, total distribution. 
Mean of total distribution, 95.522 ; mean of defectives, 
94.7. 

Standard deviation of total distribution, 30.67. 



56 A Study of the Relation of Some Physical Defects 
i (1 — a) = .4888, i (1 + a) =.5112, Z = .3987 

_ L 822_ ^4888 . _ 
' 30.67 .3987 

It can only be said that there is a positive association be- 
tween sound teeth and high scores in geography, slight 
stress being put on the degree of association owing to the 
smallness of the coefficient. 

TABLE XXXIII 
Correlation of Tonsils with Geography Scores 

Achievement Scores Expressed as Per Cent of Median 
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 

S . 1 ... 1 4 5 5 13 20 33 34 27 16 16 7 3 1 5 . 3 193 

D 2 4 1 1 6 9 5 14 14 7 4 2 1 2 2 __ __ __ 1 75 

T 3 _.. 1 8 6 6 19 29 38 48 41 23 20 9 4 3 7 . 4 268 

S, nondef ective ; D, defective; T, total distribution. 
Mean of total distribution, 95.52 ; mean of defectives, 
97.666. 

Standard deviation of total distribution, 30.67. 

\ (1 — a) = .2798, 4. (1 + a) =.7202, Z = .3312 

r _ -2.116 .2798 _ 05g 
r - 30.67 73312 — - 068 

There appears to be a negative association between the 
sound tonsils and geography scores. This fact is not clearly 
understood, as the association of other subjects has been 
positive. 

TABLE XXXIV 

Correlation of Nasal Obstructions with Written Composition 

Achievement Scores Expressed as Per Cent of Median 
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 Total 

S 1 _ .. 1 2 2 3 12 5 41 57 16 26 9 3 5 1 3 3 _ 190 
D 6 6 2 2 __ __ __ __ __ __ __ 16 

T 1 _.. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 3 . 206 

S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.23 ; mean of defectives, 95. 
Standard deviation of total distribution, 24.37. 



to Achievement in the Elementary School 57 

I (1 — a) = .0776, £U + a) = .9224, Z = .14453 
2. 23 . 0776 



24.37 .14453 



.049 



The association of nasal obstructions with written com- 
position scores, while positive, is less than that shown with 
other subjects. This may be due to the fact that only the 
students above the fourth grade took this test. Ayres says 
that defective tonsils decrease with age. 

TABLE XXXV 
Correlation of Eyes and Vision with Written Composition 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 Total 


S 
D 


1 _.. 1 2 2 3 11 4 42 58 17 25 7 2 5 . 3 
115 5 1321 1 


3 


__ 186 
20 








T 


1 _. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 


3 


206 



S, nondef ective ; D, defective; T, total distribution. 
Mean of total distribution, 97.23 ; mean of defectives, 
106.5. 

Standard deviation of total distribution, 24.37. 

4 (1_ a) =.0979, Ml + a) =.9021, Z = .17248 

_. -8.27 .0979 _ 102 

24.37 .17248 ' 

There is obviously a very high degree of negative associ- 
ation between sound vision and written composition. 

TABLE XXXVI 
Correlation of Teeth with Written Composition 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 Total 


S 
D 


1 1 _.. 1 .. 8 3 27 38 8 18 3 . 3 13 

2 1 3 4 2 20 25 10 10 6 3 2 __ __ 


1 
2 


118 

88 


T 


1 ... 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 


3 


206 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.23 ; mean of defectives, 
96.93. 

Standard deviation of total distribution, 24.37. 



58 A Study of the Relation of Some Physical Defects 
i (1 — a) =.1271, $ (1 + a) =.5729, Z = .392 

. 30 . 4271 



24. 37 . 392 



= .012 



Consistent with what has been found with other subjects, 
the association of teeth and composition is positive, but 
slight. 

TABLE XXXVII 

Correlation of Hearing with Written Composition 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 Total 


S 
D 


1 _.. 1 2 1 3.12" 4 44' 60 15 25 8 2 5 1 3 

1 13-33311 


3 


190 
16 










T 


1 _.. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 


3 


206 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.23 ; mean of defectives, 
98.75. 

Standard deviation of total distribution, 24.37. 

i (1 — a) = .0776, J (1 + a) =.9224, Z = .14453 

-1.52 .0776 



24.37 .14453 



-.033 



This is relatively a small coefficient, but is positive, and 
indicates some degree of association between hearing and 
composition. 

TABLE XXXVIII 

Correlation op Tonsils with Written Composition 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 


170 


180 Total 


S 
D 


1 _. 1 1 2 3 10 4 31 47 16 23 5 1 5 1 2 
1 2 1 16 16 2 5 4 2 . 1 


1 
2 


154 
52 


T 


1 _.. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 


3 


206 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.23 ; mean of defectives, 
98.26. 

Standard deviation of total distribution, 24.37. 



to Achievement in the Elementary School 59 

I (1 — a) = .4, h (1 + a) = .6, Z = .279 

1_ 24T37 .279 " -° 68 

Except in the case of arithmetic and reading comprehen- 
sion, this is the largest coefficient of association shown with 
tonsils. 

TABLE XXXIX 
Correlation of Eyes and Vision with Arithmetic Scores 











Achievement Scores 


Expressed as Per Cent 


of Median 











10 


20 


30 40 50 60 70 80 90 


100 110 120 130 140 


150 


160 170 


180 


190 


200 Total 


s 
D 


1 


2 
1 


9 


16 11 16 23 28 31 29 

113 8 4 2 7 


24 26 24 12 11 
3 2 13 1 


1 


4 7 
2 


4 
1 


4 
1 


7 297 
1 43 


T 


1 


3 


9 


17 12 19 31 32 33 3G 


27 28 25 15 12 


8 


6 7 


5 


5 


8 340 



S, nonclef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.44 ; mean of defectives, 
97.79. 

Standard deviation of total distribution, 42.54. 

j (1 — a) =.1264, HI + a) =.8736, Z = .2071 

_=_35 .1264 

r - 42.54 72071 -— 005 

The association of sound vision with ability in arithmetic 
is both negative and negligible. 



TABLE XL 
Correlation of Tonsils with Arithmetic Scores 



Achievement Scores Expressed as Per Cent of Median 




il 


10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


1 


2 
1 


5 
3 


1 7 15 27 24 18 26 16 18 19 10 9 5 4 7 3 
9 5 4 4 8 15 10 11 10 6 5 3 3 2 2 


3 
2 


2 231 
6 109 


T 


1 


3 


B 


17 12 19 31 32 33 36 27 28 25 15 12 8 6 7 


5 


8 340 



S, nondef ective ; D, defective; T, total distribution. 
Mean of total distribution, 97.441 ; mean of defectives, 
90.138. 

Standard deviation of total distribution, 42.54. 



60 A Study of the Relation of Some Physical Defects 
i (1 — a) = .3206, i (1 + a) =.6794, Z = .358 

7.203 .3206 _ 1Fn 

r- ~ 42.45 .358 " ' 

This coefficient shows a rather high degree of positive 
association between sound tonsils and arithmetic scores — 
much higher than the corresponding coefficients with other 
subjects. 

TABLE XLI 

Correlation of Nasal Obstructions with Low Scores in 
Arithmetic 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


2 
1 


9 


16 12 15 30 27 28 34 24 27 25 15 12 8 6 7 5 
1 4 15 5 2 3 1 


5 


8 317 
23 










T 


__ 3 


9 


17 13 19 31 32 33 36 27 28 25 15 12 8 6 7 5 


5 


8 340 



S, nondefective ; D, defective; T, total distribution. 
Mean of total distribution, 97.41 ; mean of defectives, 
77.2. 

Standard deviation of total distribution, 42.54. 

£ (1 — a) = .0676, i( + a)=.9324, Z = .130492 

,2021 .0676 _ 

" 42.54 .130492 

There is a very significant association between nasal ob- 
struction and low grades. If a pupil has such defects, he is 
probably poor in arithmetic. 

TABLE XLII 

Correlation of Teeth with Arithmetic Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


1 2 
__ 1 


6 

4 


12 8 9 13 20 18 21 15 11 16 8 6 3 5 5 3 
5 4 10 18 12 15 15 12 17 9 7 6 5 1 2 3 


2 
3 


5 209 
3 131 


T 


1 3 


10 


17 12 19 31 32 33 36 27 28 25 15 12 8 6 7 6 


5 


8 340 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.441 ; mean of defectives, 
98.046. 

Standard deviation of total distribution, 42.54. 



to Achievement in the Elementary School 61 

HI — a) = .4441, HI + a) =.5559, Z ,= .395 

.605 .4441 Ma 

Y= -&M T395" -° 16 

This is the only negative association of teeth with sub- 
jects found thus far. It is too small to be of much signifi- 
cance. 

TABLE XLIII 
Correlation of Hearing with Arithmetic Scores 



Achievement Scores Expressed as Per Cent of Median 




10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 

I) 


1 3 9 16 12 18 28 30 28 36 26 27 24 13 12 S 5 7 5 
1 1325 1112 _1 


5 


8 322 
18 










T 


1 3 9 17 12 19 31 32 33 36 27 28 25 15 12 8 6 7 5 


5 


8 340 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.441 ; mean of defectives, 
91.111. 

Standard deviation of total distribution, 42.54. 

i (1 — a) = .05294, |( + a) = .04706, Z = .1118 

6.330 .05294 



42.54 .1118 



= .0704 



Thus there is a positive association between acuteness of 
hearing and arithmetic scores. A child that hears well is 
more likely to make high scores than one that does not. 



TABLE XLIV 
Correlation of Tonsils with Writing 



Achievement Scores Expressed as Per Cent of Median 




30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 200 Total 


S 
D 


1 6 6 26 47 45 63 56 30 27 7 9 2 7 4 
1 2 9 14 20 24 15 11 6 1 2 4 2 __ 1 


4 310 
2 114 


T 


1 7 8 35 61 65 87 71 41 33 8 11 6 9 . 


6 421 



S, nondef ective ; D, defective; T, total distribution. 
Mean of total distribution, 98.561; mean of defectives, 
99.396. 

Standard deviation of total distribution, 29.08. 



62 A Study of the Relation of Some Physical Defects 
H — a) =.2681, | (1 + a) = .7319, Z = .3302 

.175 .2681 _ <0()4 



29.08 .3302 

It will be seen from this table and those that follow that 
the association of writing with defects is slight ; for tonsils 
it is negative. 

TABLE XLV 

Correlation op Eyes and Vision with Writing 





Achievement Scores 


Expressed as Per Cent 


of Median 






30 40 50 GO 70 80 90 


100 110 120 


130 140 


150 


160 170 


180 


190 200 Total 


s 

D 


1 7 7 30 57 59 79 
: 15 4 6 8 


66 36 30 
5 5 3 


8 11 


6 


2 11 


4 
1 


6 384 
40 










T 


1 7 8 35 61 65 87 


71 41 33 


8 11 


6 


9 __ 


5 


6 424 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 98.561 ; mean of defectives, 
98.5. 

Standard deviation of total distribution, 29.08. 

i (1 — a) = .0943, £ (1 + a) =.9057, Z = .1692 

r= ^061 ^943 = . 001 

29.08 .1692 

The association of sound vision with writing is positive, 
but so small that it is negligible. 



TABLE XLVI 

Correlation of Nasal Obstruction with Low Writing Ability 



Achievement Scores Expressed as Per Cent of Median 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 


S 
D 


1 7 8 32 58 62 78 64 39 32 7 11 6 9 __ 5 •_ 6 395 
33397211 . 29 






T 


1 7 8 35 61 65 87 71 41 33 8 11 6 9 . 5 _ 6 424 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 98.561 ; mean of defectives, 95. 
Standard deviation of total distribution, 29.08. 



to Achievement in the Elementary School 63 

\ (1 — a) =.0683, 4(+a)=.9307, Z = .1315 

_ _ 3.561 .0683 _ nrQ 

29.08 .1315 -• 0W 

This coefficient of association, though small, is sufficiently 
large to indicate that a child with defective nasal breathing 
is likely to make lower scores than one that has no nasal 
defects. 

TABLE XLVII 
Correlation of Hearing with Writing Ability 



Achievement Scores Expressed as Per Cent of Median 




30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 200 Total 


S 
D 


1 7 8 34 60 63 83 64 39 30 7 11 6 9 5 
11247231 


5 402 
22 








T 


1 7 8 35 61 65 87 71 41 33 1 11 6 9 5 


6 424 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 98.561; mean of defectives, 
102.72. 

Standard deviation of total distribution, 29.08. 

i (1 — a) = .0518, 4(1 + a) =.9482, Z = .1057 

4.159 .0518 



29.08 .1057 



—.07 



This coefficient indicates a negative association between 
hearing and writing. 

TABLE XLVIII 
Correlation of Sound Teeth with Writing Ability 



Achievement Scores Expressed as Per Cent op Median 




30 40 50 60 70 SO 90 100 110 120 130 140 150 160 170 180 


190 200 Total 


S 
D 


1 6 5 19 42 40 49 47 23 22 6 9 4 8 . 4 
__ 1 3 16 19 25 38 24 18 11 2 2 2 1 __ 1 


5 260 
1 164 


T 


1 7 8 35 61 65 87 71 41 33 8 11 6 9 . 5 


6 424 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 98.561; mean of defectives, 
96.463. 

Standard deviation of total distribution, 29.08. 



64 A Study of the Relation of Some Physical Defects 
i (1 — a) =.3868, ± (1 + a) =.6132, Z = .3826 

2^098 .3868 ._ 074 

~ 29.08 .3836 " 

This coefficient indicates a positive association between 
sound teeth and writing ability, and probably means that a 
child with sound teeth is slightly more likely to write well 
than one with defective teeth. 

TABLE XLIX 
Correlation of Teeth with Spelling Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


5 

4 


6 
2 


9 10 13 16 20 22 41 25 36 22 11 8 6 1 5 _ 
_ 4 10 7 9 24 31 13 21 11 5 5 1 


1 


5 261 
__ 148 


T 


9 


8 


9 14 23 23 29 46 72 38 57 33 16 13 6 15 1 


1 


5 409 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.885 ; mean of defectives, 
93.717. 

Standard deviation of total distribution, 33.41. 

x (1 — a) =.3518, £ (1 + a) =.6482, Z = .3711 

4,168 .3518 __ 

" 33.41 .3711 " ' 

This coefficient shows that there is a slight positive asso- 
ciation between sound teeth and spelling scores, but is too 
small to be very significant. 

TABLE L 

Correlation of Nasal Obstructions with Low Spelling Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


9 


8 


8 11 22 19 27 44 64 38 54 31 16 13 6 1 5 1 
1314228 3 2 


1 


5 283 
26 










T 


9 


8 


9 14 23 23 29 46 72 38 57 33 16 13 6 1 5 1 


1 


5 309 



S, nondef ective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.885 ; mean of defectives, 
83.10. 

Standard deviation of total distribution, 33.41. 



to Achievement in the Elementary School 65 

£ (1 — a) =.0635, | (1 + a) =.9365, Z = .1237 

_ 14.785 .0635 __ 22? 
33.41 .1237 " 

This coefficient indicates rather a high degree of associ- 
ation between nasal obstruction and low scores. 

TABLE LI 

Correlation of Eyes and Vision with Spelling Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


9 


8 


9 10 21 20 25 42 63 32 49 29 15 12 6 1 3 1 
_423449 6 8 4 1 1____ 2 „ 


1 


4 360 
1 49 


T 


9 


8 


9 14 23 23 29 46 72 38 57 33 16 13 6 1 5 1 


1 


5 409 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.885 ; mean of defectives, 
99.625. 

Standard deviation of total distribution, 33.41. 

I (1 — a) =.1198, H 1 + a)=.8802, Z = .1988 

1.74 .1198 



33.41 .1988 



= —.031 



This coefficient shows a negative association between 
vision and high spelling scores. It is probably large enough 
to be significant. 

TABLE LII 
Correlation of Tonsils with Spelling Scores 









Achievement Scores 


Expressed as Per Cent of Median 








10 


20 


30 40 50 60 70 80 90 


100 110 120 130 140 150 160 170 180 


190 


200 Total 


s 

D 


7 
2 


6 
2 


7 8 20 19 18 38 55 
2 6 3 4 11 8 17 


29 44 28 14 8 3 1 3 __ 
9 13 5253 __21 


1 


5 314 
95 


T 


9 


s 


9 14 23 23 29 46 72 


38 57 33 16 13 6 1 5 1 


1 


5 409 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.885; mean of defectives, 
94.158. 

Standard deviation of total distribution, 33.41. 



66 A Study of the Relation of Some Physical Defects 
i(l _a) =.2322, i(l + a) =,7678, Z = .3056 
3.727 .2322 



r = 



33.41 



.3056 



.0837 



There is a relatively significant association between sound 
tonsils and high spelling scores. 

TABLE LIII 
Correlation of Hearing with Spelling Scores 



Achievement Scores Expressed as Per Cent of Median 




10 


20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 


200 Total 


S 
D 


9 


8 


8 13 22 21 28 45 67 36 54 32 15 13 6 1 4 1 
11121152 31 1_„ 1 


1 


5 389 
20 


T 


9 


8 


9 14 23 23 29 46 72 38 57 33 16 13 6 1 5 1 


1 


5 409 



S, nondefective ; D, defective ; T, total distribution. 
Mean of total distribution, 97.885 ; mean of defectives, 
94.5. 

Standard deviation of total distribution, 33.41. 



i (l_a) = .0489, £.(1 + a) =.9511, Z 

3.385 .0489 



.1005 



r = 



33.41 



.1005 



.055 



This coefficient shows a positive association between 
acuteness of hearing and high spelling scores. 



TABLE LIV 

Summary of Coefficients of Association Between Each Physical 
Defect and the Various Subjects 



-Defects- 



Subjects 



Tonsils 



Eyes, 
Vision 



Nasal 
Defects 



Teeth Hearing 



Trabue Completion ___ 

Reading Rate 

Reading Compr'ension. 

Spelling 

Geography 

Writing 

Arithmetic 

Composition 



.0962 
.044 
-.071 
.08 
-.058 
-.004 
.151 
.068 



.045 

.0758 

.0076 

.031 

.114 

.001 

.005 

.192 



.026 
.244 
.043 
.227 
.139 
.063 
.246 
.049 



.029 
.157 
.124 
.011 
.032 
.074 
.016 
.0122 



.090 
.123 

—.011 
.055 
.148 

—.070 
.070 

—.033 



Summary of Indicated Associations of Defects with Spe- 
cial Subjects. — From Table LIV it can be clearly seen that, 
on the whole, a positive association exists between defects 



to Achievement in the Elementary School 67 

and special abilities. The one noticeable exception is the 
negative association of sound vision with five of the eight 
subjects mentioned. The subjects least affected by phys- 
ical defects are Trabue completion and writing. Writing 
is more or less mechanical, and it was observed that there 
was considerable uniformity in the answers to the sim- 
plest tests in composition, while comparatively few tried the 
more difficult ones except in the higher grades. It seems 
from the table that the five major defects, in order of their 
positive association with low scores, or, stated in the oppo- 
site way, in order of their negative association with high 
scores, are nasal defects, hearing, teeth, tonsils, and vision. 



CHAPTER V 

other factors 

Final Analysis Using the Formula for Partial 
Correlation 

The preceding chapters have been concerned with the ap- 
parent association of physical defects with achievement 
scores, without raising the question of partial associations. 
It is the purpose of the present chapter to consider the influ- 
ence of such factors, as intelligence, attendance, and re- 
tardation on the association of defects with school prog- 
ress, as indicated by achievement scores. The coefficients 
tabulated in Chapter IV are to be freed from the influences 
of these factors by the use of Karl Pearson's formula. The 
application of this formula to partial correlations is fully 
explained in Chapter III, page 38. The Illinois tests were 
used to measure intelligence. These were given to all chil- 
dren above the third grade. In the first and second grades 
the Holly completion tests were used. All intelligence scores 
were reduced to per cents of class medians, as explained 
in Chapter III. One hundred per cent was arbitrarily 
taken as the dividing line between those making high scores 
and those making low scores. Almost any other percentage 
score might have been the dividing point used in the four- 
fold classification. As may be seen from Table LV, the 
distribution of both the defectives and nondefectives is suf- 
ficiently normal to prevent a marked change of results 
should the dividing line be shifted. 

table lv 
Correlation op General Defects with Intelligence Scores 



Intelligence Scores Reduced to Per Cent op Medians 







10 20 


30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 


190 200 Total 


s 

D 


2 
1 


1 1 

2 __ 


3 2 12 14 13 32 36 31 21 11 6 1 3 1 1 2 
2 1 6 22 25 40 65 31 28 14 3 4 2 1 1 


4 197 
248 






T 


3 


3 1 


5 3 18 36 38 72 101 62 49 25 9 5 5 2 2 2 


4 445 



S, nondefective ; D, Defective ; T, total distribution. 

r = .054 

For use in partial correlations Q is more nearly com- 
parable than r, with the data shown in Table XIII. It may 



to Achievement in the Elementary School 



69 



foe found from the fourfold classification shown in Table 
LVI. If 100% be taken as the dividing line between high 
and low scores, Q is found to equal .139. 1 

TABLE LVI 
Correlation of General Defects with Intelligence Scores 





Scores Abort 100 1 < 


Scores Below 100% 


Totals 


Without Defects 


AB, 81 


Ab, 116 


197 


With Defects 


aB, 84 


ab, 162 


246 


Total 


165 


178 


443 



Q = .139 



TABLE LVII 
Correlation of Special Defects with Intelligence Scores 



Defects Ab 

Hearing 189 

Nasal Obstruction 193 

Vision 193 

Teeth 130 

Tonsils 156 

General Defects 116 



AB 



aB 



llli 



192 


8 


17 


.36 


192 


13 


16 


.10 


175 


24 


16 


—.246 


131 


66 


78 


.08 


153 


47 


52 


.04 


81 


84 


162 


1.39 



For the sake of brevity, Table LVII is made to include 
the association coefficients between intelligence and each of 
the five major defects. 

Partial correlations also require coefficients of correla- 
tions between intelligence scores and achievement scores. 
When worked out by the Pearson formula, the correlation 
between intelligence and achievement was found to be .24 ± 
.03. Again, for the sake of comparison, Q is used instead 
of r, and is found to be .32. Table LVIII shows the origi- 
nal Q's in column 1, while the same coefficients, after being 
freed from the influence of intelligence as a factor, are 
shown in column 2. The method of deriving these partial 
coefficients has already been fully explained in Chapter III, 
page 38. 

'To test the effect of taking some other line of division between high and low 
scores, in the fourfold classification, 95% was taken instead, with a result that Q 
varied only in the third decimal place, being .134. 



70 A Study of the Relation of Some Physical Defects 

TABLE LVIII 

Showing Original and Partial Correlations Obtained by Freeing 
the Former from the Influence of Intelligence as a Factor 

• Q Freed from 
Defects Correlated with General Achievement Original Q Intelligence 

Tonsils .138 .122 

Vision .029 .0102 

Nasal Obstructions .799 .811 

Teeth .302 .294 

Hearing .351 .266 

General Defects .210 .175 



It will be noticed that the changes brought about by par- 
tial correlations are relatively slight. Only one — that of 
association of nasal obstructions with achievement scores — 
is increased. The latter coefficient is extremely large, indi- 
cating a high probability that even an intelligent child ad- 
dicted to mouth breathing will be backward in school work. 
The association between vision and achievement is still 
shown to be small ; in fact, it is negligible. 

The second factor to be considered before arriving at a 
final conclusion concerning the influence of physical defects 
on achievement scores is that of retardation. The measure 
of retardation used in this study is the educational quotient. 
This coefficient is obtained by dividing the normal age of 
the grade in which the child is found by the chronological 
age of the child. These are expressed as percentages and 
distributed according to the scheme for fourfold classifica- 
tion. For this grouping, educational quotients of 100 or 
above were considered high, and below 100 low. The four 
classes, then, were: high educational quotients without de- 
fects, high educational quotients with defects, low educa- 
tional quotients without defects, and low educational quo- 
tients with defects. From these fourfold classifications the 
quotients shown in Table LX, column 1, were derived. 
Before these coefficients can be used with those of column 
2, Table LVIII, they must be freed from the influence of 
intelligence. This is done by the use of the same formula 
referred to in the last section, with results shown in column 
2 of Table LX. It will be observed from these coeffi- 
cients that there is a positive association between physical 
defects and retardation in every case, except that of eyes, 
or vision. Here the association is negative and sufficiently 
large to be significant. This probably means that retarded 
children have stronger vision than normal or accelerated 
children, while other defectives are more often retarded 
than are the normal children. Thus it becomes necessary 



to Achievement in the Elementary School 



71 



to consider these facts in connection with the problem of 
defects and achievement scores. 



TABLE LIX 
Educational Quotient Correlated with General Ability 





Scores Above 100% 


Scores Below 100% 


Totals 


Educational Quotient 
above 100% 


AB, 90 


Ab, 41 


131 


Educational Quotient 
below 100% 


aB, 135 


ab, 80 


215 


Total 


225 


121 


346 



Q = .131 

Q with intelligence eliminated, 

Q = .095 

TABLE LX 
Correlation of Educational Quotients with Physical Soundness 

Q Freed from 
Original Q Intelligence 

Tonsils .142 .138 

Vision —.181 —.154 

Nasal Obstruction .169 .158 

Teeth .509 .535 

Hearing .099 .055 

General Defects .379 .126 



TABLE LXI 

Original and Derived Correlation Coefficients with Physical 
Defects and Achievement 



Original Q 

Tonsils .138 

Vision .029 

Nasal Obstructions .799 

Teeth .302 

Hearing .351 

General Defects .210 



Q with Influence Q with Influence 
of Intelligence of Retardation 



Eliminated 


Eliminated 


.222 


.110 


.010 


.024 


.811 


.814 


.294 


.289 


.266 


.262 


.175 


.126 



72 A Study of the Relation of Some Physical Defects 

Table LXI, column 3, is a summary of results obtained 
after this factor had been eliminated. On the whole, the 
changes made in the coefficients are not very great, the 
most noticeable one being that of the association of general 
defects with achievement scores, which drops from .175 to 
.126. The association coefficients are now all positive and 
sufficiently large to be significant. The least significant of 
all is the association of vision with defects. The most sig- 
nificant is the association of nasal obstructions with 
achievement. It may be observed that the latter has in- 
creased with every elimination and finally reaches a maxi- 
mum of .814. This indicates the extreme necessity of med- 
ical treatment for this class of students if results are to be 
expected from their school work. Teeth and hearing are 
of about equal importance as handicaps to progress, the 
former having slight ascendency over the latter. Both co- 
efficients are large enough to indicate a serious problem 
for the physical supervisor. 

The third factor that should be mentioned in connection 
with the association of defects with scores is that of attend- 
ance. It is usually conceded that there is a high degree of 
association between attendance and promotion, which leads 
to retardation. Ayres makes the statement that an attend- 
ance of less than three-fourths full time usually means a 
failure of promotion. 1 Strayer and Thorndyke 2 say that, 
on the whole, the effect of absence is small until very large 
amounts of absence are reached. Reavis 3 considers it a 
subject of prime importance to the school administrator. 

The correlation of days attended by the Humboldt chil- 
dren with standard test scores has been worked out from 
the distributions shown in Table LXII below. It may be 
seen from this distribution that the average number of days 
attended per child is high. In fact, the median is 163.9 
out of a total of 176. This high attendance is explained by 
the fact that the data for this study were collected during 
the last two weeks of the school term. The children that 
were there at that time were those that had been regular in 
attendance. 



1 Ayres, L. P., Laggards in Our Schools, page 136. 

2 Strayer and Thorndyke, Educational Administration, Macmillan Company, 1914, 
page 42. 

3 Reavis, G. H., Factors Controlling Attendance in Rural Schools. 



to Achievement in the Elementary School 



73 



TABLE LXII 
Attendance Correlated with Scores 





10 


20 


30 


40 


50 


60 


70 1 80 1 90 


100 


110 


120 


130 


140 


150 


160 


170 


T 


0- 


















1 












2 


3 


10— . - 

20 

30 _ 


1 
1 

1 


1 
1 






1 
1 




2 
3 

1 

1 


1 


1 
1 

1 

3 


1 

1 
3 

1 




2 

1 
4 
4 
4 
9 
5 
2 
2 
2 

1 


1 

1 
1 

6 
10 

10 
21 
10 

7 
5 

1 

1 


5 

8 

10 

23 

22 

20 

11 

7 

4 

1 

1 


1 

1 

3 

12 

14 

23 

37 

23 

27 

5 

3 
2 

1 
1 
2 


1 
4 


40 — 

50 

60 

70 


1 
1 


1 
1 
3 
1 


1 

1 

1 

1 

1 


1 

1 
1 
3 

2 
3 
1 
1 


3 
11 
35 
43 


80 


70 


90 _ 

100 


102 
63 


110 


1 1 
1 


49 


120 
130 


27 

7 


140 


5 


150 _. 


4 


160 


3 


170 


1 


180 — _ 


1 


Above 180 








■ 


3 



Totals ! 3| 3j lj 0| 2| 2| 6| 7| 1] 7| 6| 5| 13| 36] 74] 112] 157|435 

This uniformity in the group as to attendance almost 
eliminates attendance as a factor. The coefficient of cor- 
relation, worked out from Table LXII, is found to be — .01, 
which is really negligible. The coefficient of association 
between attendance and defects for the group was found to 
be only .08. If these coefficients are used with the one for 
defects and scores, Table LXI, a partial coefficient with 
the factor of attendance eliminated may be found. If 1, 2, 
and 3 represent achievement scores, defects, and attendance, 
respectively, 



then Qv> = .126; Qk 



and Qi-.-o = 



126 



01 



01; Qas 

,08) 



08 



(1 .0001) *(1— .0064) 



127 



Thus the coefficient of .127 is found to differ from the 
original .126 in the third decimal place only, which is really 
a negligible difference. None of the coefficients shown in 
Table LXI were found to be materially changed by the elim- 
ination of attendance as a factor. In view of this fact, it 
has been deemed expedient, for the sake of brevity, to disre- 
gard attendance as a factor. So the final conclusions drawn 
from this study are to be based on the results tabulated in 
column 3, Table LXI. 



CHAPTER VI 
SUMMARY AND CONCLUSIONS 

Summary. — In the introductory chapter it was pointed 
out that while for almost a century medical and physical 
inspection had been practiced in Europe, they did not be- 
come very frequent in America until about the beginning of 
the present century. It was also pointed out that much 
confusion has from the first resulted from a lack of agree- 
ment as to the purpose, the technique, and the interpreta- 
tion of the results of these examinations. The need for 
uniform and concerted action has been stressed along with 
the need of objective interpretation. It was shown that 
this is now made possible by the introduction of standard 
tests and measures, but that it had been difficult to make 
objective a method that was based to so large an extent upon 
teachers' estimates. Objective tests not only make testing 
scientific, but make results comparable for the country at 
large. 

Chapter I has briefly outlined those studies that by their 
nature form a background for the present one. Chapter II 
emphasizes the importance of the problem and points out 
the three aims of the study as, first, calling attention to 
the relation of physical defects to school progress as a wide 
field for fruitful research ; second, application of the math- 
ematical technique of attributes to problems of school ad- 
ministration ; and, third, the interpretation of the results 
obtained from the data used in the study by means of coeffi- 
cients of association. The first of these has been realized 
by pointing out the lack of objective literature on the sub- 
ject and by calling attention to the indicated association of 
defects with successful school work. The second has been 
demonstrated by concrete application of the fourfold, mani- 
fold, and mean square contingency formulae to the data used 
in this study. In Chapter III especially has particular 
pains been taken to emphasize and visualize each step, so as 
to give the reader not only a reading knowledge of the for- 
mulae, but a working knowledge as well. The third pur- 
pose — namely, the interpretation of the results of this 
study — has been carried out in part by a brief interpreta- 
tion of each association quotient as soon as derived, and in a 
general way in the conclusions following this summary. 

In addition to indicating the probable association of gen- 
eral defects with general ability, Chapter IV has under- 



to Achievement in the Elementary School 75 

taken to indicate the association of each defect with each 
subject included in the elementary school. These results 
are shown in separate tables and summarized in tabular 
form at the close of the chapter. 

Chapter V undertakes to account for the influence of at- 
tendance, intelligence, and retardation as factors in achieve- 
ment and to eliminate the influence of these factors from 
the coefficients of association. This has been done by means 
of partial correlations in the case of each of the major de- 
fects. These factors have also been eliminated from the 
coefficient of general defects with general ability. The final 
results, together with the original coefficients, are shown in 
tabular form in Table LXI. 

Conclusions. — Physical defects are directly associated 
with low scores 1 Physical defects constitute "a" cause of 
retardation. 2 It has been shown that retardation consti- 
tutes a cause of backwardness in achievement. 3 Then 
physical defects both directly and indirectly constitute a 
cause of backwardness in achievement. 

All defects do not constitute handicaps to progress to the 
same degree. In this respect they should probably be 
ranked in the following order: 4 nasal obstruction and mouth 
breathing with which it is accompanied, defective teeth and 
the resulting maladies, defective hearing, defective tonsils, 
and defective eyes, which includes both defective eyes and 
defective vision. The last named appears to be only slightly 
associated with low scores or backwardness in subjects. In 
fact, in connection with many subjects the association is 
shown to be negative. 5 In other words, it can hardly be 
said that vision follows the same rules as do other defects. 
But, in general, the defective child is somewhat more liable 
to make low scores than is the physically sound one under 
the same conditions. 

The objective evidence presented in the early part of 
this study shows that physical defects are widespread ; 6 in 
the latter part it is shown that these materially affect school 
work, 7 while the two lead to the conclusion that there would 
be a gain — financial, social, and otherwise — by the elimina- 
tion of such defects as are capable of prevention or removal 
by medical science. 

The application of the theory of attributes, together with 
the association formulae, to an administrative problem of 



1 This statement is based upon Table LXI. 

2 See Table LX. 

3 See Table LIX. 

4 See Table LXI. 

5 See Table LIV. 

°See Tables II and III. 

7 See Table LXI. 



76 A Study of the Relation of Some Physical Defects 

this kind, is both scientific 1 and desirable as an aid to the 
method of variables usually employed. That it is practica- 
ble is demonstrated by its application to the present study. 

Figures, while having distinct values as revealing general 
tendencies, must not be interpreted as showing with abso- 
lute precision either the sum total effect of physical handi- 
caps or, in the case of individual defects, the exact relative 
retarding force of each. But the indication may be taken 
as significant. It is very probable that there are complex 
associations among the various defects themselves, the exact 
nature or degree of which is not yet known. Neither is it 
known to what extent or with what ratio, constant or vary- 
ing, the retarding force of a defect increases as the defect 
becomes more serious. These offer themselves as field for 
further study. Factors not dealt with here, such as home 
environment or heredity, without doubt play an important 
part both in explaining the cause of defects and in the force 
with which they impede progress. These, too, are problems 
full of promise to the research student. 

From the results of this study it is evident that the field 
open to the health supervisor of the school is full of oppor- 
tunities to serve humanity by conserving the physical sound- 
ness of the rising generations. He can greatly increase the 
possibilities of many pupils in his charge. He can at least 
make their work easier and their lives happier and more 
successful by insistent and persistent discharge of his duty. 
And yet he, too, has his limitations. Doubtless, Ayres 2 is 
correct when he so forcefully says: "The long-yearned-for 
royal road to learning is not always to be found through 
the surgeon's knife. 'It has not been demonstrated that if 
you cut out a child's tonsils, fit him with a pair of eyeglasses, 
and clear him of adenoids, the school term will be cut in 
half, the general level of education will surge up, and the 
city will save millions of dollars.' The old-fashioned vir- 
tues of industry, application, intelligence, and regularity still 
hold sway, and among the reasons for poor scholarship are 
still to be found such old stand-bys as age upon starting, 
absence, laziness, and stupidity." 

Suggested Further Studies 

1. The influence of heredity on the association of physical 
defects with achievement scores. 

2. The influence of environment on the association of 
physical defects with achievement scores. 

3. The influence of the personal equation on the reliabil- 
ity of the physical examiner's report. 

4. The interrelation of the physical defects and the prob- 
able effect of multiplicity of defects in a single individual. 

^Yule, Chapter I. 

-Laggards in Our Schools, Ayres. 



to Achievement in the Elementary School 77 

BIBLIOGRAPHY 

I. On Method: 

1. Biometrika, Volume II : 

a. Correlation Tables: Correlation in Lesser Celondine. 

These tables illustrate unequally the best forms for 
representing- data, page 154. 

b. Sheppard's Tables: W. F. Sheppard. These tables are 

indispensable in the use of Karl Pearson's formula for 
one variable and, one attribute, page 182. 

c. Also many other illustrations and applications of va- 

rious formulae for attributes. 

2. Biometrika, Volume VII : 

a. Karl Pearson's formula? for correlating one variable 

with an attribute, page 97; correlation of physical de- 
fects and weight, page 102; also his interpretation of 
a coefficient as "significant," page 103. 

b. Karl Pearson: A New Method, with one variable given 

by alternative and the other by multiple categories, 
page 248. 

c. Elderton, Ethel M. Galton, Eugenics Laboratory: Asso- 

ciation of Drawing with Other Capacities in School 
Children. Gives coefficients and makes statement that 
Q is not comparable with r unless the latter is in- 
creased 40% to 60%. 

3. Peterson, Dr. Joseph: Method of Interpreting Results in the 

Cleveland Arithmetic Tests. Contains an explanation 
of grouping data by means of average percentages, 
enabling the score from several tests to be combined 
into a general ability score. 

4. Rugg, H. O. : Statistical Method Applied to Education. 

Formulae for mean square contingencies. 

5. Yule, G. U.: Introduction to the Theory of Statistics. This 

is probably the most helpful reference on use of at- 
tributes. Chapters I to III, inclusive. Griffity & Co., 
London. 

II. Previous Objective Studies: 

1. Gulick and Ayres: Medical Inspection of Schools. Russell 

Sage Foundation Publication. Fuli of valuable infor- 
mation on method and results of physical and medical 
examinations. 

2. Ayres, L. P.: Laggards in Our Schools. Russell Sage Foun- 

dation Publication. Full of information on causes of 
retardation, using teachers' estimates and promotions 
as basis of study. Physical defects one cause of re- 
tardation. 

3. Cornell, W. S.: Defects Among Exempt and Nonexempt 

Children. Psychological Clinic, January 15, 1908. 
Based on teachers' marks. 

4. Allpors, Frank, Chairman of Committee on Conservation of 

Vision, Chicago. Pamphlet entitled, School Children's 
Eyes. This is not an objective study, but a report. 

5. Albert E. Taussig, M.D., Clinic St. Louis County, Mo.: 

Physical Examination of Public School Children. 
Very good objective report of percentages of defec- 
tives and relation to teachers' reports. 



78 A Study of the Relation of Some Physical Defects 

6. Bureau of Education Bulletin, No. 4, 1919: A Manual of 

Educational Legislation. Contains valuable mention 
of history of medical examinations and laws in differ- 
ent states. 

7. Bureau of Education Bulletin, No. 13, page 28, 1919: Review 

of Educational Legislation. Contains valuable men- 
tion of the history of the movement and state laws. 

8. Ruml et al. : Methods and Results of Testing School Chil- 

dren. E. P. Dutton Company, New York. Gives data 
on defects and Whipple tests, but does not work out 
association coefficients for same. A second volume is 
promised. 

9. Cornell, W. S. : Classification of pupils on the bases of "nor- 

mal," "fair," "bad" vision in relation to school sub- 
jects, showing difference in percentages based on 
teachers' marks. 

III. Related Subjects: 

Berkowitz, J. H. : The Eyesight of School Children. Defective 
vision as related to environment. Bureau of Education Bul- 
letin, 1919, No. 65. 

Heilman, J. D. : A Clinic Examination Blank for Backward 
Children in the Public Schools. Psychological Clinic, De- 
cember 15, 1907. 

Newmayer, S. W. : The Trained Nurse in the Public Schools 
as a Factor in Education of the Children. American Journal 
of Nursing, December, 1906. 

Tyler, John N. : Abstract of Eight Lectures on the Physical 
Basis of Education. Twentieth-Century Club, Boston, 1906. 

Effect of Study on the Eyesight. Popular Scientific Monthly, 
Volume XXII, page 74. 

Effect of Student Life Upon Eyesight. Circular No. 6, Bu- 
reau of Education, page 29. 

Psychological Clinic, Volume I, No. 1, March 15, 1907. (Most 
scientific exponent of the work for backward and mentally 
retarded children.) 

Terman, L. M. : Hygiene of School Children. Houghton, Mifflin 
& Co., New York. 

Dressier, F. B., and Kinsley, S. C. : Open-Air Schools. Rather 
complete history of the movement from Germany to America. 
On page 228 is also found a quotation from Ayres as to the 
number of failures among defectives. 

Englis: Principles of Secondary Education, Chapters I to IV. 
Thinks there is high correlation between physical well-being 
and achievements. 

Cubberley: Public-School Administration, Chapter XX. 

Dutton and Sneddon: Administration of Public Education in the 
United States, pages 96, 394, 439, 47. 

Dressier, F. B., United States Commissioner of Education, Bul- 
letin, 1913, Volume I, pages 415-434. 

Baker, Josephine: Physical Condition of Retarded Children. 
Fourth International Congress on School Hygiene, Volume 
IV, 1913. Twenty-five per cent of retarded due to personal 
illness; eighty-nine per cent of children defective. Does 
not correlate. 




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